FlatlandA romance of
many dimensions

With
Illustrations by the Author, A SQUARE(Edwin A.
Abbott 1838-1926)

ToThe
Inhabitants of SPACE IN GENERALAnd H. C. IN PARTICULARThis Work is DedicatedBy a Humble
Native of FlatlandIn the Hope thatEven as he
was Initiated into the MysteriesOf THREE DimensionsHaving been
previously conversantWith ONLY TWOSo the
Citizens of that Celestial RegionMay aspire
yet higher and higherTo the
Secrets of FOUR FIVE OR EVEN SIX DimensionsThereby contributingTo the
Enlargement of THE IMAGINATIONAnd the
possible DevelopmentOf that most
rare and excellent Gift of MODESTYAmong the
Superior RacesOf SOLID HUMANITY

PREFACE TO THE
SECOND AND REVISED EDITION, 1884. BY THE EDITOR

If my poor
Flatland friend retained the vigour of mind which he enjoyed when he
began to compose these Memoirs, I should not now need to represent
him in this preface, in which he desires, firstly, to return his
thanks to his readers and critics in Spaceland, whose appreciation
has, with unexpected celerity, required a second edition of his work;
secondly, to apologize forcertain errors and misprints (for which,
however, he is not entirely responsible); and, thirdly, to explain
one or two misconceptions. But he is not the Square he once was.
Years of imprisonment, and the still heavier burden of general
incredulity and mockery, have combined with the natural decay of old
age to erase from his mind many of the thoughts and notions, and much
also of the terminology, which he acquired during his short stay in
Spaceland. He has, therefore, requested me to reply in his behalf to
two special objections, one of an intellectual, the other of a moral nature.

The first
objection is, that a Flatlander, seeing a Line, sees something that
must be thick to the eye as well as long to the eye (otherwise it
would not be visible, if it had not some thickness); and consequently
he ought (it is argued) to acknowledge that his countrymen are not
only long and broad, but also (though doubtless in a very slight
degree) thick or high. His objection is plausible, and, to
Spacelanders, almost irresistible, so that, I confess, when I first
heard it, I knew not what to reply. But my poor old friend's answer
appears to me completely to meet it.

"I
admit," said he - when I mentioned to him this objection -
"I admit the truth of your critic's facts, but I deny his
conclusions. It is true that we have really in Flatland a Third
unrecognized Dimension called `height,' just as it is also true that
you have really in Spaceland a Fourth unrecognized Dimension, called
by no name at present, but which I will call `extra-height'. But we
can no more take cognizance of our `height' then you can of your
`extra-height'. Even I - who have been in Spaceland, and have had the
privilege of understanding for twenty-four hours the meaning of
`height' - even I cannot now comprehend it, nor realize it by the
sense of sight or by any process of reason; I can but apprehend it by faith.

"The
reason is obvious. Dimension implies direction, implies measurement,
implies the more and the less. Now, all our lines are equally and
infinitesimally thick (or high, whichever you like); consequently,
there is nothing in them to lead our minds to the conception of that
Dimension. No `delicate micrometer' - as has been suggested by one
too hasty Spaceland critic - would in the least avail us; for we
should not know what to measure, nor in what direction. When we see a
Line, we see something that is long and bright; brightness, as well
as length, is necessary to the existence of a Line; if the brightness
vanishes, the Line is extinguished. Hence, all my Flatland friends -
when I talk to them about the unrecognized Dimension which is somehow
visible in a Line - say, `Ah, you mean brightness': and when I reply,
`No, I mean a real Dimension,' they at once retort `Then measure it,
or tell us in what direction it extends'; and this silences me, for I
can do neither. Only yesterday, when the Chief Circle (in other words
our High Priest) came to inspect the State Prison and paid me his
seventh annual visit, and when for the seventh time he put me the
question, `Was I any better?' I tried to prove to him that he was
`high,' as well as long and broad, although he did not know it. But
what was his reply? `You say I am "high"; measure my
"highness" and I will believe you.' What could I do? How
could I meet his challenge? I was crushed; and he left the room triumphant.

"Does this
still seem strange to you? Then put yourself in a similar position.
Suppose a person of the Fourth Dimension, condescending to visit you,
were to say, `Whenever you open your eyes, you see a Plane (which is
of Two Dimensions) and you infer a Solid (which is of Three); but in
reality you also see (though you do not recognize) a Fourth
Dimension, which is not colour nor brightness nor anything of the
kind, but a true Dimension, although I cannot point out to you its
direction, nor can you possibly measure it.' What would you say to
such a visitor? Would not you have him locked up? Well, that is my
fate: and it is as natural for us Flatlanders to lock up a Square for
preaching the Third Dimension, as it is for you Spacelanders to lock
up a Cube for preaching the Fourth. Alas, how strong a family
likeness runs through blind and persecuting humanity in all
Dimensions! Points, Lines, Squares, Cubes, Extra- Cubes - we are all
liable to the same errors, all alike the Slaves of our respective
Dimensional prejudices, as one of your Spaceland poets has said -

`One touch of
Nature makes all worlds akin'."1

On this, point
the defence of the Square seems to me to be impregnable. I wish I
could say that his answer to the second (or moral) objection was
equally clear and cogent. lt has been objected that he is a
woman-hater; and as this objection has been vehemently urged by those
whom Nature's decree has constituted the somewhat larger half of the
Spaceland race, I should like to remove it, so far as I can honestly
do so. But the Square is so unaccustomed to the use of the moral
terminology of Spaceland that I should be doing him an injustice if I
were literally to transcribe his defence against this charge. Acting,
therefore, as his interpreter and summarizer, I gather that in the
course of an imprisonment of seven years he has himself modified his
own personal views, both as regards Women and as regards the
Isosceles or Lower Classes. Personally, he now inclines to the
opinion of the Sphere that the Straight Lines are in many important
respects superior to the Circles. But, writing as a Historian, he has
identified himself (perhaps too closely) with the views generally
adopted by Flatland, and (as he has been informed) even Spaceland,
Historians; in whose pages (until very recent times) the destinies of
Women and of the masses of mankind have seldom been deemed worthy of
mention and never of careful consideration.

In a still more
obscure passage he now desires to disavow the Circular or
aristocratic tendencies with which some critics have naturally
credited him. While doing justice to the intellectual power with
which a few Circles for many generations maintained their supremacy
over immense multitudes of their countrymen, he believes that the
facts of Flatland, speaking for themselves without comment On his
part, declare that Revolutions cannot always be suppressed by
slaughter; and that Nature, in sentencing the Circles to infecundity,
has condemned them to ultimate failure - "and herein," he
says, "I see a fulfillment of the great Law of all worlds, that
while the wisdom of Man thinks it is working one thing, the wisdom of
Nature constrains it to work another, and quite a different and far
better thing." For the rest, he begs his readers not to suppose
that every minute detail in the daily life of Flatland must needs
correspond to some other detail in Spaceland; and yet he hopes that,
taken as a whole, his work may prove suggestive as well as amusing,
to those Spacelanders of moderate and modest minds who - speaking of
that which is of the highest importance, but lies beyond experience -
decline to say on the one hand, "This can never be," and on
the other hand, "It must needs be precisely thus, and we know
all about it."

CONTENTS

PART 1:
THIS WORLD

1. Of the
Nature of Flatland

2. Of the
Climate and Houses in Flatland

3.
Concerning the Inhabitants of Flatland

4.
Concerning the Women

5. Of our
Methods in Recognizing one another

6. Of
Recognition by Sight

7.
Concerning Irregular Figures

8. Of the
Ancient Practice of Painting

9. Of the
Universal Colour Bill

10. Of the
Suppression of the Chromatic Sedition

11.
Concerning our Priests

12. Of the
Doctrine of our Priests

PART II:
OTHER WORLDS

13. How I
had a Vision of Lineland

14. How I
vainly tried to explain the nature of Flatland

15.
Concerning a Stranger from Spaceland

16. How the
Stranger vainly endeavoured to reveal to me in words the mysteries ofSpaceland

17. How the
Sphere, having in vain tried words, resorted to deeds

18. How I
came to Spaceland and what I saw there

19. How,
though the Sphere shewed me other mysteries of Spaceland, I still
desired more; and what came of it

20. How the
Sphere encouraged me in a Vision

21. How I
tried to teach the Theory of Three Dimensions to to my Grandson, and
with what success

22. How I
then tried to diffuse the Theory of Three Dimensions by other means,
and of the result

Part I: This World

"Be
patient, for the world is broad and wide."

1. Of the
Nature of Flatland

I CALL our
world Flatland, not because we call it so, but to make its nature
clearer to you, my happy readers, who are privileged to live in Space.

Imagine a vast
sheet of paper on which straight Lines, Triangles, Squares,
Pentagons, Hexagons, and other figures, instead of remaining fixed in
their places, move freely about, on or in the surface, but without
the power of rising above or sinking below it, very much like shadows
- only hard and with luminous edges - and you will then have a pretty
correct notion of my country and countrymen. Alas, a few years ago, I
should have said "my universe": but now my mind has been
opened to higher views of things.

In such a
country, you will perceive at once that it is impossible that there
should be anything of what you call a "solid" kind; but I
dare say you will suppose that we could at least distinguish by sight
the Triangles, Squares, and other figures, moving about as I have
described them. On the contrary, we could see nothing of the kind,
not at least so as to distinguish one figure from another. Nothing
was visible, nor could be visible, to us, except Straight Lines; and
the necessity of this I will speedily demonstrate.

Place a penny
on the middle of one of your tables in Space; and leaning over it,
look down upon it. It will appear a circle.

But now,
drawing back to the edge of the table, gradually lower your eye (thus
bringing yourself more and more into the condition of the inhabitants
of Flatland), and you will find the penny becoming more and more oval
to your view; and at last when you have placed your eye exactly on
the edge of the table (so that you are, as it were, actually a
Flatlander) the penny will then have ceased to appear oval at all,
and will have become, so far as you can see, a straight line.

The same thing
would happen if you were to treat in the same way a Triangle, or
Square, or any other figure cut out of pasteboard. As soon as you
look at it with your eye on the edge on the table, you will find that
it ceases to appear to you a figure, and that it becomes in
appearance a straight line. Take for example an equilateral Triangle
- who represents with us a Tradesman of the respectable class. Fig. 1
represents the Tradesman as you would see him while you were bending
over him from above; figs. 2 and 3 represent the Tradesman, as you
would see him if your eye were close to the level, or all but on the
level of the table; and if your eye were quite on the level of the
table (and that is how we see him in Flatland) you would see nothing
but a straight line.

When I was in
Spaceland I heard that your sailors have very similar experiences
while they traverse your seas and discern some distant island or
coast lying on the horizon. The far-off land may have bays,
forelands, angles in and out to any number and extent; yet at a
distance you see none of these (unless indeed your sun shines bright
upon them revealing the projections and retirements by means of light
and shade), nothing but a grey unbroken line upon the water.

Well, that is
just what we see when one of our triangular or other acquaintances
comes toward us in Flatland. As there is neither sun with us, nor any
light of such a kind as to make shadows, we have none of the helps to
the sight that you have in Spaceland. If our friend comes closer to
us we see his line becomes larger; if he leaves us it becomes
smaller: but still he looks like a straight line; be he a Triangle,
Square, Pentagon, Hexagon, Circle, what you will - a straight Line he
looks and nothing else. You may perhaps ask how under these
disadvantageous circumstances we are able to distinguish our friends
from one another: but the answer to this very natural question will
be more fitly and easily given when I come to describe the
inhabitants of Flatland. For the present let me defer this subject,
and say a word or two about the climate and houses in our country.

2. Of the
Climate and Houses in Flatland

AS WITH you, so
also with us, there are four points of the compass North, South,
East, and West.

There being no
sun nor other heavenly bodies, it is impossible for us to determine
the North in the usual way; but we have a method of our own. By a Law
of Nature with us, there is a constant attraction to the South; and,
although in temperate climates this is very slight - so that even a
Woman in reasonable health can journey several furlongs northward
without much difficulty - yet the hampering effect of the southward
attraction is quite sufficient to serve as a compass in most parts of
our earth. Moreover, the rain (which falls at stated intervals)
coming always from the North, is an additional assistance; and in the
towns we have the guidance of the houses, which of course have their
side-walls running for The most part North and South, so that the
roofs may keep off the rain from the North. In the country, where
there are no houses, the trunks of the trees serve as some sort of
guide. Altogether, we have not so much difficulty as might be
expected in determining our bearings.

Yet in our more
temperate regions, in which the southward attraction is hardly felt,
walking sometimes in a perfectly desolate plain where there have been
no houses nor trees to guide me, I have been occasionally compelled
to remain stationary for hours together, waiting till the rain came
before continuing my journey. On the weak and aged, and especially on
delicate Females, the force of attraction tells much more heavily
than on the robust of the Male Sex, so that it is a point of
breeding, if you meet a Lady in the street, always to give her the
North side of the way - by no means an easy thing to do always at
short notice when you are in rude health and in a climate where it is
difficult to tell your North from your South.

Windows there
are none in our houses: for the light comes to us alike in our homes
and out of them, by day and by night, equally at all times and in all
places, whence we know not. It was in old days, with our learned men,
an interesting and oft-investigated question, "What is the
origin of light?" and the solution of it has been repeatedly
attempted, with no other result than to crowd our lunatic asylums
with the would-be solvers. Hence, after fruitless attempts to
suppress such investigations indirectly by making them liable to a
heavy tax, the Legislature, in comparatively recent times, absolutely
prohibited them. I - alas; I alone in Flatland - know now only too
well the true solution of this mysterious problem; but my knowledge
cannot be made intelligible to a single one of my countrymen; and I
am mocked at - I, the sole possessor of the truths of Space and of
the theory of the introduction of Light from the world of three
Dimensions - as if I were the maddest of the mad! But a truce to
these painful digressions: let me return to our houses.

The most common
form for the construction of a house is five- sided or pentagonal, as
in the annexed figure. The two Northern sides RO, OF, constitute the
roof, and for the most part have no doors; on the East is a small
door for the Women; on the West a much larger one for the Men; the
South side or floor is usually doorless.

Square and
triangular houses are not allowed, and for this reason. The angles of
a Square (and still more those of an equilateral Triangle,) being
much more pointed than those of a Pentagon, and the lines of
inanimate objects (such as houses) being dimmer than the lines of Men
and Women, it follows that there is no little danger lest the points
of a square or triangular house residence might do serious injury to
an inconsiderate or perhaps absent-minded traveller suddenly
therefore, running against them: and as early as the eleventh century
of our era, triangular houses were universally forbidden by Law, the
only exceptions being fortifications, powder- magazines, barracks,
and other state buildings, which it is not desirable that the general
public should approach without circumspection.

At this period,
square houses were still everywhere permitted, though discouraged by
a special tax. But, about three centuries afterwards, the Law decided
that in all towns containing a population above ten thousand, the
angle of a Pentagon was the smallest house- angle that could be
allowed consistently with the public safety. The good sense of the
community has seconded the efforts of the Legislature; and now, even
in the country, the pentagonal construction has superseded every
other. It is only now and then in some very remote and backward
agricultural district that an antiquarian may still discover a square house.

3. Concerning
the Inhabitants of Flatland

THE GREATEST
length or breadth of a full grown inhabitant of Flatland may be
estimated at about eleven of your inches. Twelve inches may be
regarded as a maximum.

Our Women are
Straight Lines.

Our Soldiers
and Lowest Classes of Workmen are Triangles with two equal sides,
each about eleven inches long, and a base or third side so short
(often not exceeding half an inch) that they form at their vertices a
very sharp and formidable angle. Indeed when their bases are of the
most degraded type (not more than the eighth part of an inch in
size). they can hardly be distinguished from Straight Lines or Women;
so extremely pointed are their vertices. With us, as with you, these
Triangles are distinguished from others by being called Isosceles;
and by this name I shall refer to them in the following pages.

Our Middle
Class consists of Equilateral or Equal-Sided Triangles.

Our
Professional Men and Gentlemen are Squares (to which class I myself
belong) and Five-Sided Figures or Pentagons.

Next above
these come the Nobility, of whom there are several degrees, beginning
at Six-Sided Figures, or Hexagons, and from thence rising in the
number of their sides till they receive the honourable title of
Polygonal, or many-sided. Finally when the number of the sides
becomes so numerous, and the sides themselves so small, that the
figure cannot be distinguished from a circle, he is included in the
Circular or Priestly order; and this is the highest class of all.

It is a Law of
Nature with us that a male child shall have one more side than his,
father, so that each generation shall rise (as a rule) one step in
the scale of development and nobility. Thus the son of a Square is a
Pentagon; the son of a Pentagon, a Hexagon; and so on.

But this rule
applies not always to the Tradesmen, and still less often to the
Soldiers, and to the Workmen; who indeed can hardly be said to
deserve the name of human Figures, since they have not all their
sides equal. With them therefore the Law of Nature does not hold; and
the son of an Isosceles (i.e. a Triangle with two sides equal)
remains Isosceles still. Nevertheless, all hope is not shut out, even
from the Isosceles, that his posterity may ultimately rise above his
degraded condition. For, after a long series of military successes,
or diligent and skilful labours, it is generally found that the more
intelligent among the Artisan and Soldier classes manifest a slight
increase of their third side or base, and a shrinkage of the two
other sides. Intermarriages (arranged by the Priests) between the
sons and daughters of these more intellectual members of the lower
classes generally result in an offspring approximating still more to
the type of the Equal-Sided Triangle.

Rarely - in
proportion to the vast numbers of Isosceles births - is a genuine and
certifiable Equal-Sided Triangle produced from Isosceles parents.2
Such a birth requires, as its antecedents, not only a series of
carefully arranged intermarriages, but also a long, continued
exercise of frugality and self-control on the part of the would-be
ancestors of the coming Equilateral, and a patient, systematic, and
continuous development of the Isosceles intellect through many generations.

The birth of, a
True Equilateral Triangle from Isosceles parents is the subject of
rejoicing in our country for many furlongs around. After a strict
examination conducted by the Sanitary and Social Board, the infant,
if certified as Regular, is with solemn ceremonial admitted into the
class of Equilaterals. He is then immediately taken from his proud
yet sorrowing parents and adopted by some childless Equilateral, who
is bound by oath never to permit the child henceforth to enter his
former home or so much as to look upon his relations again, for fear
lest the freshly developed organism may, by force of unconscious
imitation, fall back again into his hereditary level.

The occasional
emergence of an Equilateral from the ranks of his serf-born ancestors
is welcomed, not only by the poor serfs themselves, as a gleam of
light and hope shed upon the monotonous squalor of their existence,
but also by the Aristocracy at large; for all the higher classes are
well aware that these rare phenomena, while they do little or nothing
to vulgarize their own privileges, serve as a most useful barrier
against revolution from below.

Had the
acute-angled rabble been all, without exception, absolutely destitute
of hope and of ambition, they might have found leaders in some of
their many seditious outbreaks, so able as to render their superior
numbers and strength too much even for the wisdom of the Circles. But
a wise ordinance of Nature has decreed that, in proportion as the
working-classes increase in intelligence, knowledge, and all virtue,
in that same proportion their acute angle (which makes them
physically terrible) shall increase also and approximate to the
comparatively harmless angle of the Equilateral Triangle. Thus, in
the most brutal and formidable of the soldier class - creatures
almost on a level with women in their lack of intelligence - it is
found that, as they wax in the mental ability necessary to employ
their tremendous penetrating power to advantage, so do they wane in
the power of penetration itself.

How admirable
is this Law of Compensation! And how perfect a proof of the natural
fitness and, I may almost say, the divine origin of the aristocratic
constitution of the States in Flatland! By a judicious use of this
Law of Nature, the Polygons and Circles are almost always able to
stifle sedition in its very cradle, taking advantage of the
irrepressible and boundless hopefulness of the human mind. Art also
comes to the aid of Law and Order. It is generally found possible -
by a little artificial compression or expansion on the part of the
State physicians - to make some of the more intelligent leaders of a
rebellion perfectly Regular, and to admit them at once into the
privileged classes; a much larger number, who are still below the
standard, allured by the prospect of being ultimately ennobled, are
induced to enter the State Hospitals, where they are kept in
honourable confinement for life; one or two alone of the more
obstinate, foolish, and hopelessly irregular are led to execution.

Then the
wretched rabble of the Isosceles, planless and leaderless, are either
transfixed without resistance by the small body of their brethren
whom the Chief Circle keeps in pay for emergencies of this kind; or
else more often, by means of jealousies and suspicions skilfully
fomented among them by the Circular party, they are stirred to mutual
warfare, and perish by one another's angles. No less than one hundred
and twenty rebellions are recorded in our annals, besides minor
outbreaks numbered at two hundred and thirty-five; and they have all
ended thus.

4. Concerning
the Women.

IF OUR highly
pointed Triangles of the Soldier class are formidable, it may be
readily inferred that far more formidable are our Women. For if a
Soldier is a wedge, a Woman is a needle; being, so to speak, all
point, at least at the two extremities. Add to this the power of
making herself practically invisible at will, and you will perceive
that a Female, in Flatland, is a creature by no means to be trifled with.

But here,
perhaps, some of my younger Readers may ask how a woman in Flatland
can make herself invisible. This ought, I think, to be apparent
without any explanation. However, a few words will make it clear to
the most unreflecting.

Place a needle
on a table. Then, with your eye on the level of the table, look at it
side-ways, and you see the whole length of it; but look at it
end-ways, and you see nothing but a point, it has become practically
invisible. Just so is it with one of our Women. When her side is
turned towards us, we see her as a straight line; when the end
containing her eye or mouth - for with us these two organs are
identical - is the part that meets our eye, then we see nothing but a
highly lustrous point; but when the back is presented to our view,
then - being only sub-lustrous, and, indeed, almost as dim as an
inanimate object - her hinder extremity serves her as a kind of
Invisible Cap.

The dangers to
which we are exposed from our Women must now be manifest to the
meanest capacity in Spaceland. If even the angle of a respectable
Triangle in the middle class is not without its dangers; if to run
against a Working Man involves a gash; if collision with an officer
of the military class necessitates a serious wound; if a mere touch
from the vertex of a Private Soldier brings with it danger of death;
- what can it be to run against a Woman, except absolute and
immediate destruction? And when a Woman is invisible, or visible only
as a dim sub-lustrous point, how difficult must it be, even for the
most cautious, always to avoid collision!

Many are the
enactments made at different times in the different States of
Flatland, in order to minimize this peril; and in the Southern and
less temperate climates where the force of gravitation is greater,
and human beings more liable to casual and involuntary motions, the
Laws concerning Women are naturally much more stringent. But a
general view of the Code may be obtained from the following summary: -

Every house
shall have one entrance in the Eastern side, for the use of Females
only; by which all females shall enter "in a becoming and
respectful manner"3 and not by the Men's or Western door.

No Female shall
walk in any public place without continually keeping up her
Peace-cry, under penalty of death.

Any Female,
duly certified to be suffering from St. Vitus's Dance, fits, chronic
cold accompanied by violent sneezing, or any disease necessitating
involuntary motions, shall be instantly destroyed .

In some of the
States there is an additional Law forbidding Females, under penalty
of death, from walking or standing in any public place without moving
their backs constantly from right to left so as to indicate their
presence to those behind them; others oblige a Woman, when
travelling, to be followed by one of her sons, or servants, or by her
husband; others confine Women altogether to their houses except
during the religious festivals. But it has been found by the wisest
of our Circles or Statesmen that the multiplication of restrictions
on Females tends not only to the debilitation and diminution of the
race, but also to the increase of domestic murders to such an extent
that a State loses more than it gains by a too prohibitive Code.

For whenever
the temper of the Women is thus exasperated by confinement at home or
hampering regulations abroad, they are apt to vent their spleen upon
their husbands and children; and in the less temperate climates the
whole male population of a village has been sometimes destroyed in
one or two hours of simultaneous female outbreak. Hence the Three
Laws, mentioned above, suffice for the better regulated States, and
may be accepted as a rough exemplification of our Female Code.

After all, our
principal safeguard is found, not in Legislature, but in the
interests of the Women themselves. For, although they can inflict
instantaneous death by a retrograde movement, yet unless they can at
once disengage their stinging extremity from the struggling body of
their victim, their own frail bodies are liable to be shattered.

The power of
Fashion is also on our side. I pointed out that in some less
civilized States no female is suffered to stand in any public place
without swaying her back from right to left. This practice has been
universal among ladies of any pretensions to breeding in all
well-governed States, as far back as the memory of Figures can reach.
It is considered a disgrace to any State that legislation should have
to enforce what ought to be, and is in every respectable female, a
natural instinct. The rhythmical and, if I may so say, well-
modulated undulation of the back in our ladies of Circular rank is
envied and imitated by the wife of a common Equilateral, who can
achieve nothing beyond a mere monotonous swing, like the ticking of a
pendulum; and the regular tick of the Equilateral is no less admired
and copied by the wife of the progressive and aspiring Isosceles, in
the females of whose family no "back-motion" of any kind
has become as yet a necessity of life. Hence, in every family of
position and consideration, "back motion" is as prevalent
as time itself; and the husbands and sons in these households enjoy
immunity at least from invisible attacks.

Not that it
must be for a moment supposed that our Women are destitute of
affection. But unfortunately the passion of the moment predominates,
in the Frail Sex, over every other consideration. This is, of course,
a necessity arising from their unfortunate conformation. For as they
have no pretensions to an angle, being inferior in this respect to
the very lowest of the Isosceles, they are consequently wholly devoid
of brain-power, and have neither reflection, judgment nor
forethought, and hardly any memory. Hence, in their fits of fury,
they remember no claims and recognize no distinctions. I have
actually known a case where a Woman has exterminated her whole
household, and half an hour afterwards, when her rage was over and
the fragments swept away, has asked what has become of her husband
and her children.

Obviously then
a Woman is not to be irritated as long as she is in a position where
she can turn round. When you have them in their apartments - which
are constructed with a view to denying them that power - you can say
and do what you like; for they are then wholly impotent for mischief,
and will not remember a few minutes hence the incident for which they
may be at this moment threatening you with death, nor the promises
which you may have found it necessary to make in order to pacify
their fury.

On the whole we
get on pretty smoothly in our domestic relations, except in the lower
strata of the Military Classes. There the want of tact and discretion
on the part of the husbands produces at times indescribable
disasters. Relying too much on the offensive weapons of their acute
angles instead of the defensive organs of good sense and seasonable
simulations, these reckless creatures too often neglect the
prescribed construction of the women's apartments, or irritate their
wives by ill-advised expressions out of doors, which they refuse
immediately to retract. Moreover a blunt and stolid regard for
literal truth indisposes them to make those lavish promises by which
the more judicious Circle can in a moment pacify his consort. The
result is massacre; not, however, without its advantages, as it
eliminates the more brutal and troublesome of the Isosceles; and by
many of our Circles the destructiveness of the Thinner Sex is
regarded as one among many providential arrangements for suppressing
redundant population, and nipping Revolution in the bud.

Yet even in our
best regulated and most approximately Circular families I cannot say
that the ideal of family life is so high as with you in Spaceland.
There is peace, in so far as the absence of slaughter may be called
by that name, but there is necessarily little harmony of tastes or
pursuits; and the cautious wisdom of the Circles has ensured safety
at the cost of domestic comfort. In every Circular or Polygonal
household it has been a habit from time immemorial - and now has
become a kind of instinct among the women of our higher classes -
that the mothers and daughters should constantly keep their eyes and
mouths towards their husband and his male friends; and for a lady in
a family of distinction to turn her back upon her husband would be
regarded as a kind of portent, involving loss of status. But, as I
shall soon shew, this custom, though it has the advantage of safety,
is not without its disadvantages.

In the house of
the Working Man or respectable Tradesman - where the wife is allowed
to turn her back upon her husband, while pursuing her household
avocations - there are at least intervals of quiet, when the wife is
neither seen nor heard, except for the humming sound of the
continuous Peace-cry; but in the homes of the upper classes there is
too often no peace. There the voluble mouth and bright penetrating
eye are ever directed to wards the Master of the household; and light
itself is not more persistent than the stream of feminine discourse.
The tact and skill which suffice to avert a Woman's sting are unequal
to the task of stopping a Woman's mouth; and as the wife has
absolutely nothing to say, and absolutely no constraint of wit,
sense, or conscience to prevent her from saying it, not a few cynics
have been found to aver that they prefer the danger of the
death-dealing but inaudible sting to the safe sonorousness of a
Woman's other end.

To my readers
in Spaceland the condition of our Women may seem truly deplorable,
and so indeed it is. A Male of the lowest type of the Isosceles may
look forward to some improvement of his angle, and to the ultimate
elevation of the whole of his degraded caste; but no Woman can
entertain such hopes for her sex. "Once a Woman, always a
Woman" is a Decree of Nature; and the very Laws of Evolution
seem suspended in her disfavour. Yet at least we can admire the wise
Prearrangement which has ordained that, as they have no hopes, so
they shall have no memory to recall, and no forethought to
anticipate, the miseries and humiliations which are at once a
necessity of their existence and the basis of the constitution of Flatland.

5. Of our
Methods of Recognizing one another.

YOU, WHO are
blessed with shade as well as light, you, who are gifted with two
eyes, endowed with a knowledge of perspective, and charmed with the
enjoyment of various colours, you, who can actually see an angle, and
contemplate the complete circumference of a Circle in the happy
region of the Three Dimensions - how shall I make clear to you the
extreme difficulty which we in Flatland experience in recognizing one
another's configuration?

Recall what I
told you above. All beings in Flatland, animate or inanimate, no
matter what their form, present to our view the same, or nearly the
same, appearance, viz. that of a straight Line. How then can one be
distinguished from another, where all appear the same?

The answer is
threefold. The first means of recognition is the sense of hearing;
which with us is far more highly developed than with you, and which
enables us not only to distinguish by the voice our personal friends,
but even to discriminate between different classes, at least so far
as concerns the three lowest orders, the Equilateral, the Square, and
the Pentagon - for of the Isosceles I take no account. But as we
ascend in the social scale, the process of discriminating and being
discriminated by hearing increases in difficulty, partly because
voices are assimilated, partly because the faculty of
voice-discrimination is a plebeian virtue not much developed among
the Aristocracy. And wherever there is any danger of imposture we
cannot trust to this method. Amongst our lowest orders, the vocal
organs are developed to a degree more than correspondent with those
of hearing, so that an Isosceles can easily feign the voice of a
Polygon, and, with some training, that of a Circle himself. A second
method is therefore more commonly resorted to.

Feeling is,
among our Women and lower classes - about our upper classes I shall
speak presently - the principal test of recognition, at all events
between strangers, and when the question is, not as to the
individual, but as to the class. What therefore
"introduction" is among the higher classes in Spaceland,
that the process of "feeling" is with us. "Permit me
to ask you to feel and be felt by my friend Mr. So-and-so" - is
still, among the more old- fashioned of our country gentlemen in
districts remote from towns, the customary formula for a Flatland
introduction. But in the towns, and among men of business, the words
"be felt by" are omitted and the sentence is abbreviated
to, "Let me ask you to feel Mr. So-and- so"; although it is
assumed, of course, that the "feeling" is to be reciprocal.
Among our still more modern and dashing young gentlemen - who are
extremely averse to superfluous effort and supremely indifferent to
the purity of their native language - the formula is still further
curtailed by the use of "to feel" in a technical sense,
meaning, "to recommend-for-the-purposes-of-feeling-and-
being-felt"; and at this moment the "slang" of polite
or fast society in the upper classes sanctions such a barbarism as
"Mr. Smith, permit me to feel Mr. Jones."

Let not my
Reader however suppose that "feeling" is with us the
tedious process that it would be with you, or that we find it
necessary to feel right round all the sides of every individual
before we determine the class to which he belongs. Long practice and
training, begun in the schools and continued in the experience of
daily life, enable us to discriminate at once by the sense of touch,
between the angles of an equal-sided Triangle, Square, and Pentagon;
and I need not say that the brainless vertex of an acute angled
Isosceles is obvious to the dullest touch. It is therefore not
necessary, as a rule, to do more than feel a single angle of an
individual; and this, once ascertained, tells us the class of the
person whom we are addressing, unless indeed he belongs to the higher
sections of the nobility. There the difficulty is much greater. Even
a Master of Arts in our University of Wentbridge has been known to
confuse a ten- sided with a twelve-sided Polygon; and there is hardly
a Doctor of Science in or out of that famous University who could
pretend to decide promptly and unhesitatingly between a twenty-sided
and a twenty-four sided member of the Aristocracy.

Those of my
readers who recall the extracts I gave above from the Legislative
code concerning Women, will readily perceive that the process of
introduction by contact requires some care and discretion. Otherwise
the angles might inflict on the unwary Feeler irreparable injury. It
is essential for the safety of the Feeler that the Felt should stand
perfectly still. A start, a fidgety shifting of the position, yes,
even a violent sneeze, has been known before now to prove fatal to
the incautious, and to nip in the bud many a promising friendship.
Especially is this true among the lower classes of the Triangles.
With them, the eye is situated so far from their vertex that they can
scarcely take cognizance of what goes on at that extremity of their
frame. They are, moreover, of a rough coarse nature, not sensitive to
the delicate touch of the highly organized Polygon. What wonder then
if an involuntary toss of the head has ere now deprived the State of
a valuable life!

I have heard
that my excellent Grandfather - one of the least irregular of his
unhappy Isosceles class, who indeed obtained, shortly before his
decease, four out of seven votes from the Sanitary and Social Board
for passing him into the class of the Equal-sided - often deplored,
with a tear in his venerable eye, a miscarriage of this kind, which
had occurred to his great-great-great-Grandfather, a respectable
Working Man with an angle or brain of 59°30'. According to his
account, my unfortunate Ancestor, being afflicted with rheumatism,
and in the act of being felt by a Polygon, by one sudden start
accidentally transfixed the Great Man through the diagonal; and
thereby, partly in consequence of his long imprisonment and
degradation, and partly because of the moral shock which pervaded the
whole of my Ancestor's relations, threw back our family a degree and
a half in their ascent towards better things. The result was that in
the next generation the family brain was registered at only 58°,
and not till the lapse of five generations was the lost ground
recovered, the full 60° attained, and the Ascent from the
Isosceles finally achieved. And all this series of calamities from
one little accident in the process of Feeling.

At this point I
think I hear some of my better educated readers exclaim, "How
could you in Flatland know anything about angles and degrees, or
minutes? We can see an angle, because we, in the region of Space, can
see two straight lines inclined to one another; but you, who can see
nothing but one straight line at a time, or at all events only a
number of bits of straight lines all in one straight line - how can
you ever discern any angle, and much less register angles of
different sizes?"

I answer that
though we cannot see angles, we can infer them, and this with great
precision. Our sense of touch, stimulated by necessity, and developed
by long training, enables us to distinguish angles far more
accurately than your sense of sight, when unaided by a rule or
measure of angles. Nor must I omit to explain that we have great
natural helps. It is with us a Law of Nature that the brain of the
Isosceles class shall begin at half a degree, or thirty minutes, and
shall increase (if it increases at all) by half a degree in every
generation; until the goal of 60° is reached, when the condition
of serfdom is quitted, and the freeman enters the class of Regulars.

Consequently,
Nature herself supplies us with an ascending scale or Alphabet of
angles for half a degree up to 60°, Specimens of which are
placed in every Elementary School throughout the land. Owing to
occasional retrogressions, to still more frequent moral and
intellectual stagnation, and to the extraordinary fecundity of the
Criminal and Vagabond Classes, there is always a vast superfluity of
individuals of the half degree and single degree class, and a fair
abundance of Specimens up to 10°. These are absolutely destitute
of civic rights; and a great number of them, not having even
intelligence enough for the purposes of warfare, are devoted by the
States to the service of education. Fettered immovably so as to
remove all possibility of danger, they are placed in the class rooms
of our Infant Schools, and there they are utilized by the Board of
Education for the purpose of imparting to the offspring of the Middle
Classes that tact and intelligence of which these wretched creatures
themselves are utterly devoid.

In some States
the Specimens are occasionally fed and suffered to exist for several
years; but in the more temperate and better regulated regions, it is
found in the long run more advantageous for the educational interests
of the young, to dispense with food, and to renew the Specimens every
month - which is about the average duration of the foodless existence
of the Criminal class. In the cheaper schools, what is gained by the
longer existence of the Specimen is lost, partly in the expenditure
for food, and partly in the diminished accuracy of the angles, which
are impaired after a few weeks of constant "feeling." Nor
must we forget to add, in enumerating the advantages of the more
expensive system, that it tends, though slightly yet perceptibly, to
the diminution of the redundant Isosceles population - an object
which every statesman in Flatland constantly keeps in view. On the
whole therefore - although I am not ignorant that, in many popularly
elected School Boards, there is a reaction in favour of "the
cheap system" as it is called - I am myself disposed to think
that this is one of the many cases in which expense is the truest economy.

But I must not
allow questions of School Board politics to divert me from my
subject. Enough has been said, I trust, to shew that Recognition by
Feeling is not so tedious or indecisive a process as might have been
supposed; and it is obviously more trustworthy than Recognition by
hearing. Still there remains, as has been pointed out above, the
objection that this method is not without danger. For this reason
many in the Middle and Lower classes, and all without exception in
the Polygonal and Circular orders, prefer a third method, the
description of which shall be reserved for the next section.

6. Of
Recognition by Sight

I AM about to
appear very inconsistent. In previous sections I have said that all
figures in Flatland present the appearance of a straight line; and it
was added or implied, that it is consequently impossible to
distinguish by the visual organ between individuals of different
classes: yet now I am about to explain to my Spaceland critics how we
are able to recognize one another by the sense of sight.

If however the
Reader will take the trouble to refer to the passage in which
Recognition by Feeling is stated to be universal, he will find this
qualification - "among the lower classes." It is only among
the higher classes and in our temperate climates that Sight
Recognition is practised.

That this power
exists in any regions and for any classes is the result of Fog; which
prevails during the greater part of the year in all parts save the
torrid zones. That which is with you in Spaceland an unmixed evil,
blotting out the landscape, depressing the spirits, and enfeebling
the health, is by us recognized as a blessing scarcely inferior to
air itself, and as the Nurse of arts and Parent of sciences. But let
me explain my meaning, without further eulogies on this beneficent Element.

If Fog were
non-existent, all lines would appear equally and indistinguishably
clear; and this is actually the case in those unhappy countries in
which the atmosphere is perfectly dry and. transparent. But wherever
there is a rich supply of Fog objects that are at a distance, say of
three feet, are appreciably dimmer than those at a distance of two
feet eleven inches; and the result is that by careful and constant
experimental observation of comparative dimness and clearness, we are
enabled to infer with great exactness the configuration of the object observed.

An instance
will do more than a volume of generalities to make my meaning clear.

Suppose I see
two individuals approaching whose rank I wish to ascertain. They are,
we will suppose, a Merchant and a Physician, or in other words, an
Equilateral Triangle and a Pentagon: how am I to distinguish them?

It will be
obvious, to every child in Spaceland who has touched the threshold of
Geometrical Studies, that, if I can bring my eye so that its glance
may bisect an angle (A) of the approaching stranger, my view will lie
as it were evenly between his two sides that are next to me (viz. CA
and ab), so that I shall contemplate the two impartially, and both
will appear of the same size.

Now in the case
of (I) the Merchant, what shall I see? I shall see a straight line
dae, in which the middle point (A) Will be very bright because it is
nearest to me; but on either side the line will shade away rapidly
into dimness, because the sides AC and AB recede rapidly into the fog
and what appear to me as the Merchant's extremities, viz. D and E,
will be very dim indeed.

On the other
hand in the case of (2) the Physician, though I shall here also see a
line (D' A' E') with a bright centre (A'), yet it will shade away
less rapidly into dimness, because the sides (A' C', A' B') recede
less rapidly into the fog: and what appear to me the Physician's
extremities, viz. D' and E', will not be not so dim as the
extremities of the Merchant.

The Reader will
probably understand from these two instances how - after a very long
training supplemented by constant experience - it is possible for the
well-educated classes among us to discriminate with fair accuracy
between the middle and lowest orders, by the sense of sight. If my
Spaceland Patrons have grasped this general conception, so far as to
conceive the possibility of it and not to reject my account as
altogether incredible - I shall have attained all I can reasonably
expect. Were I to attempt further details I should only perplex. Yet
for the sake of the young and inexperienced, who may perchance infer
- from the two simple instances I have given above, of the manner in
which I should recognize my Father and my Sons - that Recognition by
sight is an easy affair, it may be needful to point out that in
actual life most of the problems of Sight Recognition are far more
subtle and complex.

If for example,
when my Father, the Triangle, approaches me, he happens to present
his side to me instead of his angle, then, until I have asked him to
rotate, or until I have edged my eye round him, I am for the moment
doubtful whether he may not be a Straight Line, or, in other words, a
Woman. Again, when I am in the company of one of my two hexagonal
Grandsons, contemplating one of his sides (AB) full front, it will be
evident from the accompanying diagram that I shall see one whole line
(AB) in comparative brightness (shading off hardly at all at the
ends) and two smaller lines (CA and BD) dim throughout and shading
away into greater dimness towards the extremities C and D.

But I must not
give way to the temptation of enlarging on these topics. The meanest
mathematician in Spaceland will readily believe me when I assert that
the problems of life, which present themselves to the well-educated -
when they are themselves in motion, rotating, advancing or
retreating, and at the same time attempting to discriminate by the
sense of sight between a number of Polygons of high rank moving in
different directions, as for example in a ball- room or conversazione
- must be of a nature to task the angularity of the most
intellectual, and amply justify the rich endowments of the Learned
Professors of Geometry, both Static and Kinetic, in the illustrious
University of Wentbridge, where the Science and Art of Sight
Recognition are regularly taught to large classes of the lite
of the States.

It is only a
few of the scions of our noblest and wealthiest houses, who are able
to give the time and money necessary for the thorough prosecution of
this noble and valuable Art. Even to me, a Mathematician of no mean
standing, and the Grandfather of two most hopeful and perfectly
regular Hexagons, to find myself in the midst of a crowd of rotating
Polygons of the higher classes, is occasionally very perplexing. And
of course to a common Tradesman, or Serf, such a sight is almost as
unintelligible as it would be to you, my Reader, were you suddenly
transported into our country.

In such a crowd
you could see on all sides of you nothing but a Line, apparently
straight, but of which the parts would vary irregularly and
perpetually in brightness or dimness. Even if you had completed your
third year in the Pentagonal and Hexagonal classes in the University,
and were perfect in the theory of the subject, you would still find
that there was need of many years of experience, before you could
move in a fashionable crowd without jostling against your betters,
whom it is against etiquette to ask to "feel," and who, by
their superior culture and breeding, know all about your movements,
while you know very little or nothing about theirs. In a word, to
comport oneself with perfect propriety in Polygonal society, one
ought to be a Polygon oneself. Such at least is the painful teaching
of my experience.

It is
astonishing how much the Art - or I may almost call it instinct - of
Sight Recognition is developed by the habitual practice of it and by
the avoidance of the custom of "Feeling." Just as, with
you, the deaf and dumb, if once allowed to gesticulate and to use the
hand-alphabet, will never acquire the more difficult but far more
valuable art of lipspeech and lip-reading, so it is with us as
regards "Seeing" and "Feeling." None who in early
life resort to "Feeling" will ever learn "Seeing"
in perfection.

For this
reason, among our Higher Classes, "Feeling" is discouraged
or absolutely forbidden. From the cradle their children, instead of
going to the Public Elementary schools (where the art of Feeling is
taught,) are sent to higher Seminaries of an exclusive character; and
at our illustrious University, to "feel" is regarded as a
most serious fault, involving Rustication for the first offence, and
Expulsion for the second.

But among the
lower classes the art of Sight Recognition is regarded as an
unattainable luxury. A common Tradesman cannot afford to let his son
spend a third of his life in abstract studies. The children of the
poor are therefore allowed to "feel" from their earliest
years, and they gain thereby a precocity and an early vivacity which
contrast at first most favourably with the inert, undeveloped, and
listless behaviour of the half-instructed youths of the Polygonal
class; but when the latter have at last completed their University
course, and are prepared to put their theory into practice, the
change that comes over them may almost be described as a new birth,
and in every art, science, and social pursuit they rapidly overtake
and distance their Triangular competitors.

Only a few of
the polygonal Class fail to pass the Final Test or Leaving
Examination at the University. The condition of the unsuccessful
minority is truly pitiable. Rejected from the higher class, they are
also despised by the lower. They have neither the matured and
systematically trained powers of the Polygonal Bachelors and Masters
of Arts, nor yet the native precocity and mercurial versatility of
the youthful Tradesman. The professions, the public services, are
closed against them; and though in most States they are not actually
debarred from marriage, yet they have the greatest difficulty in
forming suitable alliances, as experience shews that the offspring of
such unfortunate and ill-endowed parents is generally itself
unfortunate, if not positively Irregular.

It is from
these specimens of the refuse of our Nobility that the great Tumults
and Seditions of past ages have generally derived their leaders; and
so great is the mischief thence arising that an increasing minority
of our more progressive Statesmen are of opinion that true mercy
would dictate their entire suppression, by enacting that all who fail
to pass the Final Examination of the University should be either
imprisoned for life, or extinguished by a painless death.

But I find
myself digressing into the subject of Irregularities, a matter of
such vital interest that it demands a separate section.

7. Concerning
Irregular Figures

THROUGHOUT THE
previous pages I have been assuming - what perhaps should have been
laid down at the beginning as a distinct and fundamental proposition
- that every human being in Flatland is a Regular Figure, that is to
say of regular construction. By this I mean that a Woman must not
only be a line, but a straight line; that an Artisan or Soldier must
have two of his sides equal; that Tradesmen must have three sides
equal; Lawyers (of which class I am a humble member), four sides
equal, and, generally, that in every Polygon, all the sides must be equal.

The size of the
sides would of course depend upon the age of the individual. A Female
at birth would be about an inch long, while a tall adult Woman might
extend to a foot. As to the Males of every class, it may be roughly
said that the length of an adult's sides, when added together, is two
feet or a little more. But the size of our sides is not under
consideration. I am speaking of the equality of sides, and it does
not need much reflection to see that the whole of the social life in
Flatland rests upon the fundamental fact that Nature wills all
Figures to have their sides equal.

If our sides
were unequal our angles might be unequal. Instead of its being
sufficient to feel, or estimate by sight, a single angle in order to
determine the form of an individual, it would be necessary to
ascertain each angle by the experiment of Feeling. But life would be
too short for such a tedious grouping. The whole science and art of
Sight Recognition would at once perish; Feeling, so far as it is an
art, would not long survive; intercourse would become perilous or
impossible; there would be an end to all confidence, all forethought;
no one would be safe in making the most simple social arrangements;
in a word, civilization would relapse into barbarism.

Am I going too
fast to carry my Readers with me to these obvious conclusions? Surely
a moment's reflection, and a single instance from common life, must
convince every one that our whole social system is based upon
Regularity, or Equality of Angles. You meet, for example, two or
three Tradesmen in the street, whom you recognize at once to be
Tradesmen by a glance at their angles and rapidly bedimmed sides, and
you ask them to step into your house to lunch. This you do at present
with perfect confidence, because everyone knows to an inch or two the
area occupied by an adult Triangle: but imagine that your Tradesman
drags behind his regular and respectable vertex, a parallelogram of
twelve or thirteen inches in diagonal: - what are you to do with such
a monster sticking fast in your house door?

But I am
insulting the intelligence of my Readers by accumulating details
which must be patent to everyone who enjoys the advantages of a
Residence in Spaceland. Obviously the measurements of a single angle
would no longer be sufficient under such portentous circumstances;
one's whole life would be taken up in feeling or surveying the
perimeter of one's acquaintances. Already the difficulties of
avoiding a collision in a crowd are enough to tax the sagacity of
even a well-educated Square; but if no one could calculate the
Regularity of a single figure in the company, all would be chaos and
confusion, and the slightest panic would cause serious injuries, or -
if there happened to be any Women or Soldiers present - perhaps
considerable loss of life.

Expediency
therefore concurs with Nature in stamping the seal of its approval
upon Regularity of conformation: nor has the Law been backward in
seconding their efforts. "Irregularity of Figure" means
with us the same as, or more than, a combination of moral obliquity
and criminality with you, and is treated accordingly. There are not
wanting, it is true, some promulgators of paradoxes who maintain that
there is no necessary connection between geometrical and moral
Irregularity. "The Irregular," they say, "is from his
birth scouted by his own parents, derided by his brothers and
sisters, neglected by the domestics, scorned and suspected by
society, and excluded from all posts of responsibility, trust, and
useful activity. His every movement is jealously watched by the
police till he comes of age and presents himself for inspection; then
he is either destroyed, if he is found to exceed the fixed margin of
deviation, or else immured in a Government Office as a clerk of the
seventh class; prevented from marriage; forced to drudge at an
uninteresting occupation for a miserable stipend; obliged to live and
board at the office, and to take even his vacation under close
supervision; what wonder that human nature, even in the best and
purest, is embittered and perverted by such surroundings!"

All this very
plausible reasoning does not convince me, as it has not convinced the
wisest of our Statesmen, that our ancestors erred in laying it down
as an axiom of policy that the toleration of Irregularity is
incompatible with the safety of the State. Doubtless, the life of an
Irregular is hard; but the interests of the Greater Number require
that it shall be hard. If a man with a triangular front and a
polygonal back were allowed to exist and to propagate a still more
Irregular posterity, what would become of the arts of life? Are the
houses and doors and churches in Flatland to be altered in order to
accommodate such monsters? Are our ticket collectors to be required
to measure every man's perimeter before they allow him to enter a
theatre, or to take his place in a lecture room? Is an Irregular to
be exempted from the militia? And if not, how is he to be prevented
from carrying desolation into the ranks of his comrades? Again, what
irresistible temptations to fraudulent impostures must needs beset
such a creature! How easy for him to enter a shop with his polygonal
front foremost, and to order goods to any extent from a confiding
tradesman! Let the advocates of a falsely called Philanthropy plead
as they may for the abrogation of the Irregular Penal Laws, I for my
part have never known an Irregular who was not also what Nature
evidently intended him to be - a hypocrite, a misanthropist, and, up
to the limits of his power, a perpetrator of all manner of mischief.

Not that I
should be disposed to recommend (at present) the extreme measures
adopted in some States, where an infant whose angle deviates by half
a degree from the correct angularity is summarily destroyed at birth.
Some of our highest and ablest men, men of real genius, have during
their earliest days laboured under deviations as great as, or even
greater than, forty-five minutes: and the loss of their precious
lives would have been an irreparable injury to the State. The art of
healing also has achieved some of its most glorious triumphs in the
compressions, extensions, trepannings, colligations, and other
surgical or diaetetic operations by which Irregularity has been
partly or wholly cured. Advocating therefore a Via Media, I would lay
down no fixed or absolute line of demarcation; but at the period when
the frame is just beginning to set, and when the Medical Board has
reported that recovery is improbable, I would suggest that the
Irregular offspring be painlessly and mercifully consumed.

8. Of the
Ancient Practice of Painting

IF MY Readers
have followed me with any attention up to this point, they will not
be surprised to hear that life is somewhat dull in Flatland. I do
not, of course, mean that there are not battles, conspiracies,
tumults, factions, and all those other phenomena which are supposed
to make History interesting; nor would I deny that the strange
mixture of the problems of life and the problems of Mathematics,
continually inducing conjecture and giving the opportunity of
immediate verification, imparts to our existence a zest which you in
Spaceland can hardly comprehend. I speak now from the aesthetic and
artistic point of view when I say that life with us is dull;
aesthetically and artistically, very dull indeed.

How can it be
otherwise, when all one's prospect, all one's landscapes, historical
pieces, portraits, flowers, still life, are nothing but a single
line, with no varieties except degrees of brightness and obscurity?

It was not
always thus. Colour, if Tradition speaks the truth, once for the
space of half a dozen centuries or more, threw a transient splendour
over the lives of our ancestors in the remotest ages. Some private
individual - a Pentagon whose name is variously reported - having
casually discovered the constituents of the simpler colours and a
rudimentary method of painting, is said to have begun decorating
first his house, then his slaves, then his Father, his Sons, and
Grandsons, lastly himself. The convenience as well as the beauty of
the results commended themselves to all. Wherever Chromatistes, - for
by that name the most trustworthy authorities concur in calling him,
- turned his variegated frame, there he at once excited attention,
and attracted respect. No one now needed to "feel" him; no
one mistook his front for his back; all his movements were readily
ascertained by his neighbours without the slightest strain on their
powers of calculation; no one jostled him, or failed to make way for
him; his voice was saved the labour of that exhausting utterance by
which we colourless Squares and Pentagons are often forced to
proclaim our individuality when we move amid a crowd of ignorant Isosceles.

The fashion
spread like wildfire. Before a week was over, every Square and
Triangle in the district had copied the example of Chromatistes, and
only a few of the more conservative Pentagons still held out. A month
or two found even the Dodecagons infected with the innovation. A year
had not elapsed before the habit had spread to all but the very
highest of the Nobility. Needless to say, the custom soon made its
way from the district of Chromatistes to surrounding regions; and
within two generations no one in all Flatland was colourless except
the Women and the Priests.

Here Nature
herself appeared to erect a barrier, and to plead against extending
the innovation to these two classes. Many- sidedness was almost
essential as a pretext for the Innovators. "Distinction of sides
is intended by Nature to imply distinction of colours" - such
was the sophism which in those days flew from mouth to mouth,
converting whole towns at a time to the new culture. But manifestly
to our Priests and Women this adage did not apply. The latter had
only one side, and therefore - plurally and pedantically speaking -
no sides. The former - if at least they would assert their claim to
be really and truly Circles, and not mere high-class Polygons with an
infinitely large number of infinitesimally small sides - were in the
habit of boasting (what Women confessed and deplored) that they also
had no sides, being blessed with a perimeter of one line, or, in
other words, a Circumference. Hence it came to pass that these two
Classes could see no force in the so-called axiom about
"Distinction of Sides implying Distinction of Colour;" and
when all others had succumbed to the fascinations of corporal
decoration, the Priests and the Women alone still remained pure from
the pollution of paint.

Immoral,
licentious, anarchical, unscientific - call them by what names you
will - yet, from an aesthetic point of view, those ancient days of
the Colour Revolt were the glorious childhood of Art in Flatland - a
childhood, alas, that never ripened into manhood, nor even reached
the blossom of youth. To live was then in itself a delight, because
living implied seeing. Even at a small party, the company was a
pleasure to behold; the richly varied hues of the assembly in a
church or theatre are said to have more than once proved too
distracting for our greatest teachers and actors; but most ravishing
of all is said to have been the unspeakable magnificence of a
military review.

The sight of a
line of battle of twenty thousand Isosceles suddenly facing about,
and exchanging the sombre black of their bases for the orange and
purple of the two sides including their acute angle; the militia of
the Equilateral Triangles tricoloured in red, white, and blue; the
mauve, ultra-marine, gamboge, and burnt umber of the Square
artillerymen rapidly rotating near their vermilion guns; the dashing
and flashing of the five-coloured and six-coloured Pentagons and
Hexagons careering across the field in their offices of surgeons,
geometricians and aides-de-camp - all these may well have been
sufficient to render credible the famous story how an illustrious
Circle, overcome by the artistic beauty of the forces under his
command, threw aside his marshal's baton and his royal crown,
exclaiming that he henceforth exchanged them for the artist's pencil.
How great and glorious the sensuous development of these days must
have been is in part indicated by the very language and vocabulary of
the period. The commonest utterances of the commonest citizens in the
time of the Colour Revolt seem to have been suffused with a richer
tinge of word or thought; and to that era we are even now indebted
for our finest poetry and for whatever rhythm still remains in the
more scientific utterance of these modern days.

9. Of the
Universal Colour Bill

BUT MEANWHILE
the intellectual Arts were fast decaying.

The Art of
Sight Recognition, being no longer needed, was no longer practised;
and the studies of Geometry, Statics, Kinetics, and other kindred
subjects, came soon to be considered superfluous, and fell into
disrespect and neglect even at our University. The inferior Art of
Feeling speedily experienced the same fate at our Elementary Schools.
Then the Isosceles classes, asserting that the Specimens were no
longer used nor needed, and refusing to pay the customary tribute
from the Criminal classes to the service of Education, waxed daily
more numerous and more insolent on the strength of their immunity
from the old burden which had formerly exercised the twofold
wholesome effect of at once taming their brutal nature and thinning
their excessive numbers.

Year by year
the Soldiers and Artisans began more vehemently to assert - and with
increasing truth - that there was no great difference between them
and the very highest class of Polygons, now that they were raised to
an equality with the latter, and enabled to grapple with all the
difficulties and solve all the problems of life, whether Statical or
Kinetical, by the simple process of Colour Recognition. Not content
with the natural neglect into which Sight Recognition was falling,
they began boldly to demand the legal prohibition of all
"monopolizing and aristocratic Arts" and the consequent
abolition of all endowments for the studies of Sight Recognition,
Mathematics, and Feeling. Soon, they began to insist that inasmuch as
Colour, which was a second Nature, had destroyed the need of
aristocratic distinctions, the Law should follow in the same path,
and that henceforth all individuals and all classes should be
recognized as absolutely equal and entitled to equal rights.

Finding the
higher Orders wavering and undecided, the leaders of the Revolution
advanced still further in their requirements, and at last demanded
that all classes alike, the Priests and the Women not excepted,
should do homage to Colour by submitting to be painted. When it was
objected that Priests and Women had no sides, they retorted that
Nature and Expediency concurred in dictating that the front half of
every human being (that is to say, the half containing his eye and
mouth) should be distinguishable from his hinder half. They therefore
brought before a general and extraordinary Assembly of all the States
of Flatland a Bill proposing that in every Woman the half containing
the eye and mouth should be coloured red, and the other half green.
The Priests were to be painted in the same way, red being applied to
that semicircle in which the eye and mouth formed the middle point;
while the other or hinder semicircle was to be coloured green.

There was no
little cunning in this proposal, which indeed emanated not from any
Isosceles - for no being so degraded would have had angularity enough
to appreciate, much less to devise, such a model of state-craft - but
from an Irregular Circle who, instead of being destroyed in his
childhood, was reserved by a foolish indulgence to bring desolation
on his country and destruction on myriads of his followers.

On the one hand
the proposition was calculated to bring the Women in all classes over
to the side of the Chromatic Innovation. For by assigning to the
Women the same two colours as were assigned to the Priests, the
Revolutionists thereby ensured that, in certain positions, every
Woman would appear like a Priest, and be treated with corresponding
respect and deference - a prospect that could not fail to attract the
female Sex in a mass.

But by some of
my Readers the possibility of the identical appearance of Priests and
Women, under the new Legislation, may not be recognized; if so, a
word or two will make it obvious.

Imagine a woman
duly decorated, according to the new Code; with the front half (i.e.
the half containing eye and mouth) red, and with the hinder half
green. Look at her from one side. Obviously you will see a straight
line, half red, half green.

Now imagine a
Priest, whose mouth is at M, and whose front semicircle (AMB) is
consequently coloured red, while his hinder semicircle is green; so
that the diameter AB divides the green from the red. If you
contemplate the Great Man so as to have your eye in the same straight
line as his dividing diameter (AB), what you will see will be a
straight line (CBD), of which one half(CB) will be red, and the other
(BD) green. The whole line (CD) will be rather shorter perhaps than
that of a full-sized Woman, and will shade off more rapidly towards
its extremities; but the identity of the colours would give you an
immediate impression of identity of Class, making you neglectful of
other details. Bear in mind the decay of Sight Recognition which
threatened society at the time of the Colour Revolt; add too the
certainty that Women would speedily learn to shade off their
extremities so as to imitate the Circles; it must then be surely
obvious to you, my dear Reader, that the Colour Bill placed us under
a great danger of confounding a Priest with a young Woman.

How attractive
this prospect must have been to the Frail Sex may readily be
imagined. They anticipated with delight the confusion that would
ensue. At home they might hear political and ecclesiastical secrets
intended not for them but for their husbands and brothers, and might
even issue commands in the name of a priestly Circle; out of doors
the striking combination of red and green, without addition of any
other colours, would be sure to lead the common people into endless
mistakes, and the Women would gain whatever the Circles lost, in the
deference of the passers by. As for the scandal that would befall the
Circular Class if the frivolous and unseemly conduct of the Women
were imputed to them, and as to the consequent subversion of the
Constitution, the Female Sex could not be expected to give a thought
to these considerations. Even in the households of the Circles, the
Women were all in favour of the Universal Colour Bill.

The second
object aimed at by the Bill was the gradual demoralization of the
Circles themselves. In the general intellectual decay they still
preserved their pristine clearness and strength of understanding.
From their earliest childhood, familiarized in their Circular
households with the total absence of Colour, the Nobles alone
preserved the Sacred Art of Sight Recognition, with all the
advantages that result from that admirable training of the intellect.
Hence, up to the date of the introduction of the Universal Colour
Bill, the Circles had not only held their own, but even increased
their lead of the other classes by abstinence from the popular fashion.

Now therefore
the artful Irregular whom I described above as the real author of
this diabolical Bill, determined at one blow to lower the status of
the Hierarchy by forcing them to submit to the pollution of Colour,
and at the same time to destroy their domestic opportunities of
training in the Art of Sight Recognition, so as to enfeeble their
intellects by depriving them of their pure and colourless homes. Once
subjected to the chromatic taint, every parental and every childish
Circle would demoralize each other. Only in discerning between the
Father and the Mother would the Circular infant find problems for the
exercise of its understanding - problems too often likely to be
corrupted by maternal impostures with the result of shaking the
child's faith in all logical conclusions. Thus by degrees the
intellectual lustre of the Priestly Order would wane, and the road
would then lie open for a total destruction of all Aristocratic
Legislature and for the subversion of our Privileged Classes.

10. Of the
Suppression of Chromatic Sedition

THE AGITATION
for the Universal Colour Bill continued for three years; and up to
the last moment of that period it seemed as though Anarchy were
destined to triumph.

A whole army of
Polygons, who turned out to fight as private soldiers, was utterly
annihilated by a superior force of Isosceles Triangles - the Squares
and Pentagons meanwhile remaining neutral. Worse than all, some of
the ablest Circles fell a prey to conjugal fury. Infuriated by
political animosity, the wives in many a noble household wearied
their lords with prayers to give up their opposition to the Colour
Bill; and some, finding their entreaties fruitless, fell on and
slaughtered their innocent children and husband, perishing themselves
in the act of carnage. It is recorded that during that triennial
agitation no less than twenty three Circles perished in domestic discord.

Great indeed
was the peril. It seemed as though the Priests had no choice between
submission and extermination; when suddenly the course of events was
completely changed by one of those picturesque incidents which
Statesmen ought never to neglect, often to anticipate, and sometimes
perhaps to originate, because of the absurdly disproportionate power
with which they appeal to the sympathies of the populace.

It happened
that an Isosceles of a low type, with a brain little if at all above
four degrees - accidentally dabbling in the colours of some Tradesman
whose shop he had plundered - painted himself, or caused himself to
be painted (for the story varies) with the twelve colours of a
Dodecagon. Going into the Market Place he accosted in a feigned voice
a maiden, the orphan daughter of a noble Polygon, whose affection in
former days he had sought in vain; and by a series of deceptions -
aided, on the one side, by a string of lucky accidents too long to
relate, and on the other, by an almost inconceivable fatuity and
neglect of ordinary precautions on the part of the relations of the
bride - he succeeded in consummating the marriage. The unhappy girl
committed suicide on discovering the fraud to which she had been subjected.

When the news
of this catastrophe spread from State to State the minds of the Women
were violently agitated. Sympathy with the miserable victim and
anticipations of similar deceptions for themselves, their sisters,
and their daughters, made them now regard the Colour Bill in an
entirely new aspect. Not a few openly avowed themselves converted to
antagonism; the rest needed only a slight stimulus to make a similar
avowal. Seizing this favourable opportunity, the Circles hastily
convened an extraordinary Assembly of the States; and besides the
usual guard of Convicts, they secured the attendance of a large
number of reactionary Women.

Amidst an
unprecedented concourse, the Chief Circle of those days - by name
Pantocyclus - arose to find himself hissed and hooted by a hundred
and twenty thousand Isosceles. But he secured silence by declaring
that henceforth the Circles would enter on a policy of Concession;
yielding to the wishes of the majority, they would accept the Colour
Bill. The uproar being at once converted to applause, he invited
Chromatistes, the leader of the Sedition, into the centre of the
hall, to receive in the name of his followers the submission of the
Hierarchy. Then followed a speech, a masterpiece of rhetoric, which
occupied nearly a day in the delivery, and to which no summary can do justice.

With a grave
appearance of impartiality he declared that as they were now finally
committing themselves to Reform or Innovation, it was desirable that
they should take one last view of the perimeter of the whole subject,
its defects as well as its advantages. Gradually introducing the
mention of the dangers to the Tradesmen, the Professional Classes and
the Gentlemen, he silenced the rising murmurs of the Isosceles by
reminding them that, in spite of all these defects, he was willing to
accept the Bill if it was approved by the majority. But it was
manifest that all, except the Isosceles, were moved by his words and
were either neutral or averse to the Bill.

Turning now to
the Workmen he asserted that their interests must not be neglected,
and that, if they intended to accept the Colour Bill, they ought at
least to do so with full view of the consequences. Many of them, he
said, were on the point of being admitted to the class of the Regular
Triangles; others anticipated for their children a distinction they
could not hope for themselves. That honourable ambition would now
have to be sacrificed. With the universal adoption of Colour, all
distinctions would cease; Regularity would be confused with
Irregularity; development would give place to retrogression; the
Workman would in a few generations be degraded to the level of the
Military, or even the Convict Class; political power would be in the
hands of the greatest number, that is to say the Criminal Classes,
who were already more numerous than the Workmen, and would soon
out-number all the other Classes put together when the usual
Compensative Laws of Nature were violated.

A subdued
murmur of assent ran through the ranks of the Artisans, and
Chromatistes, in alarm, attempted to step forward and address them.
But he found himself encompassed with guards and forced to remain
silent while the Chief Circle in a few impassioned words made a final
appeal to the Women, exclaiming that, if the Colour Bill passed, no
marriage would henceforth be safe, no woman's honour secure; fraud,
deception, hypocrisy would pervade every household; domestic bliss
would share the fate of the Constitution and pass to speedy
perdition. "Sooner than this," he cried, "Come death."

At these words,
which were the preconcerted signal for action, the Isosceles Convicts
fell on and transfixed the wretched Chromatistes; the Regular
Classes, opening their ranks, made way for a band of Women who, under
direction of the Circles, moved, back foremost, invisibly and
unerringly upon the unconscious soldiers; the Artisans, imitating the
example of their betters, also opened their ranks. Meantime bands of
Convicts occupied every entrance with an impenetrable phalanx.

The battle, or
rather carnage, was of short duration. Under the skillful generalship
of the Circles almost every Woman's charge was fatal and very many
extracted their sting uninjured, ready for a second slaughter. But no
second blow was needed; the rabble of the Isosceles did the rest of
the business for themselves. Surprised, leaderless, attacked in front
by invisible foes, and finding egress cut off by the Convicts behind
them, they at once - after their manner - lost all presence of mind,
and raised the cry of "treachery." This sealed their fate.
Every Isosceles now saw and felt a foe in every other. In half an
hour not one of that vast multitude was living; and the fragments of
seven score thousand of the Criminal Class slain by one another's
angles attested the triumph of Order.

The Circles
delayed not to push their victory to the uttermost. The Working Men
they spared but decimated. The Militia of the Equilaterals was at
once called out; and every Triangle suspected of Irregularity on
reasonable grounds, was destroyed by Court Martial, without the
formality of exact measurement by the Social Board. The homes of the
Military and Artisan classes were inspected in a course of
visitations extending through upwards of a year; and during that
period every town, village, and hamlet was systematically purged of
that excess of the lower orders which had been brought about by the
neglect to pay the tribute of Criminals to the Schools and
University, and by the violation of the other natural Laws of the
Constitution of Flatland. Thus the balance of classes was again restored.

Needless to say
that henceforth the use of Colour was abolished, and its possession
prohibited. Even the utterance of any word denoting Colour, except by
the Circles or by qualified scientific teachers, was punished by a
severe penalty. Only at our University in some of the very highest
and most esoteric classes - which I myself have never been privileged
to attend - it is understood that the sparing use of Colour is still
sanctioned for the purpose of illustrating some of the deeper
problems of mathematics. But of this I can only speak from hearsay.

Elsewhere in
Flatland, Colour is now non-existent. The art of making it is known
to only one living person, the Chief Circle for the time being; and
by him it is handed down on his deathbed to none but his Successor.
One manufactory alone produces it; and, lest the secret should be
betrayed, the Workmen are annually consumed, and fresh ones
introduced. So great is the terror with which even now our
Aristocracy looks back to the far distant days of the agitation for
the Universal Colour Bill.

11. Concerning
our Priests

IT IS high time
that I should pass from these brief and discursive notes about things
in Flatland to the central event of this book, my initiation into the
mysteries of Space. That is my subject; all that has gone before is
merely preface.

For this reason
I must omit many matters of which the explanation would not, I
flatter myself, be without interest for my Readers: as for example,
our method of propelling and stopping ourselves, although destitute
of feet; the means by which we give fixity to structures of wood,
stone, or brick, although of course we have no hands, nor can we lay
foundations as you can, nor avail ourselves of the lateral pressure
of the earth; the manner in which the rain originates in the
intervals between our various zones, so that the northern regions do
not intercept the moisture from falling on the southern; the nature
of our hills and mines, our trees and vegetables, our seasons and
harvests; our Alphabet and method of writing, adapted to our linear
tablets; these and a hundred other details of our physical existence
I must pass over, nor do I mention them now except to indicate to my
readers that their omission proceeds not from forgetfulness on the
part of the author, but from his regard for the time of the Reader.

Yet before I
proceed to my legitimate subject some few final remarks will no doubt
be expected by my Readers upon those pillars and mainstays of the
Constitution of Flatland, the controllers of our conduct and shapers
of our destiny, the objects of universal homage and almost of
adoration: need I say that I mean our Circles or Priests?

When I call
them Priests, let me not be understood as meaning no more than the
term denotes with you. With us, our Priests are Administrators of all
Business, Art, and Science; Directors of Trade, Commerce,
Generalship, Architecture, Engineering, Education, Statesmanship,
Legislature, Morality, Theology; doing nothing themselves, they are
the Causes of everything worth doing, that is done by others.

Although
popularly everyone called a Circle is deemed a Circle, yet among the
better educated Classes it is known that no Circle is really a
Circle, but only a Polygon with a very large number of very small
sides. As the number of the sides increases, a polygon approximates
to a Circle; and, when the number is very great indeed, say for
example three or four hundred, it is extremely difficult for the most
delicate touch to feel any polygonal angles. Let me say rather, it
would be difficult: for, as I have shown above, Recognition by
Feeling is unknown among the highest society, and to feel a Circle
would be considered a most audacious insult. This habit of abstention
from Feeling in the best society enables a Circle the more easily to
sustain the veil of mystery in which, from his earliest years, he is
wont to enwrap the exact nature of his Perimeter or Circumference.
Three feet being the average Perimeter it follows that, in a polygon
of three hundred sides each side will be no more than the hundredth
part of a foot in length, or little more than the tenth part of an
inch; and in a Polygon of six or seven hundred sides the sides are
little larger than the diameter of a spaceland pin-head. It is always
assumed, by courtesy, that the Chief Circle for the time being has
ten thousand sides.

The ascent of
the posterity of the Circles in the social scale is not restricted,
as it is among the lower Regular classes, by the Law of Nature which
limits the increase of sides to one in each generation. If it were
so, the number of sides in a Circle would be a mere question of
pedigree and arithmetic, and the four hundred and ninety-seventh
descendant of an Equilateral Triangle would necessarily be a Polygon
with live hundred sides. But this is not the case. Nature s Law
prescribes two antagonistic decrees affecting Circular propagation;
first, that as the race climbs higher in the scale of development, so
development shall proceed at an accelerated pace; second, that in the
same proportion, the race shall become less fertile. Consequently in
the home of a Polygon of four or five hundred sides it is rare to
find a son; more than one is never seen. On the other hand the son of
a five-hundred sided Polygon has been known to possess five hundred
and fifty, or even six hundred sides.

Art also steps
in to help the process of the higher Evolution. Our physicians have
discovered that the small and tender sides of an infant Polygon of
the higher class can be fractured, and his whole frame re-set, with
such exactness that a Polygon of two or three hundred sides sometimes
- by no means always, for the process is attended with serious risk -
but sometimes overleaps two or three hundred generations, and as if
were doubles at a stroke, the number of his progenitors and the
nobility of his descent.

Many a
promising child is sacrificed in this way. Scarcely one out of ten
survives. Yet so strong is the parental ambition among those Polygons
who are, as it were, on the fringe of the Circular class, that it is
very rare to find a Nobleman of that position in society, who has
neglected to place his first-born in the Circular Neo-Therapeutic
Gymnasium before he has attained the age of a month.

One year
determines success or failure. At the end of that time the child has,
in all probability, added one more to the tombstones that crowd the
Neo-Therapeutic Cemetery; but on rare occasions a glad procession
bears back the little one to his exultant parents, no longer a
Polygon, but a Circle, at least by courtesy: and a single instance of
so blessed a result induces multitudes of Polygonal parents to submit
to similar domestic sacrifices, which have a dissimilar issue.

12. Of the
Doctrine of our Priests

AS TO the
doctrine of the Circles it may briefly be summed up in a single
maxim, "Attend to your Configuration." Whether political,
ecclesiastical, or moral, all their teaching has for its object the
improvement of individual and collective Configuration - with special
reference of course to the Configuration of the Circles, to which all
other objects are subordinated.

It is the merit
of the Circles that they have effectually Suppressed those ancient
heresies which led men to waste energy and sympathy in the vain
belief that conduct depends upon will, effort, training,
encouragement, praise, or anything else but Configuration. It was
Pantocyclus - the illustrious Circle mentioned above, as the queller
of the Colour Revolt - who first convinced mankind that Configuration
makes the man; that if, for example, you are born an Isosceles with
two uneven sides, you will assuredly go wrong unless you have them
made even - for which purpose you must go to the Isosceles Hospital;
similarly, if you are a Triangle, or Square, or even a Polygon, born
with any Irregularity, you must be taken to one of the Regular
Hospitals to have your disease cured; otherwise you will end your
days in the State Prison or by the angle of the State Executioner.

All faults or
defects, from the slightest misconduct to the most flagitious crime,
Pantocyclus attributed to some deviation from perfect Regularity in
the bodily figure, caused perhaps (if not congenital) by some
collision in a crowd; by neglect to take exercise, or by taking too
much of it; or even by a sudden change of temperature, resulting in a
shrinkage or expansion in some too susceptible part of the frame.
Therefore, concluded that illustrious Philosopher, neither good
conduct nor bad conduct is a fit subject, in any sober estimation,
for either praise or blame. For why should you praise, for example,
the integrity of a Square who faithfully defends the interests of his
client, when you ought in reality rather to admire the exact
precision of his right angles? Or again, why blame a lying, thievish
Isosceles when you ought rather to deplore the incurable inequality
of his sides?

Theoretically,
this doctrine is unquestionable; but it has practical drawbacks. In
dealing with an Isosceles, if a rascal pleads that he cannot help
stealing because of his unevenness, you reply that for that very
reason, because he cannot help being a nuisance to his neighbours,
you, the Magistrate, cannot help sentencing him to be consumed - and
there's an end of the matter. But in little domestic difficulties,
where the penalty of consumption, or death, is out of the question,
this theory of Configuration sometimes comes in awkwardly; and I must
confess that occasionally when one of my own Hexagonal Grandsons
pleads as an excuse for his disobedience that a sudden change of the
temperature has been too much for his perimeter, and that I ought to
lay the blame not on him but on his Configuration, which can only be
strengthened by abundance of the choicest sweetmeats, I neither see
my way logically to reject, nor practically to accept, his conclusions.

For my own
part, I find it best to assume that a good sound scolding or
castigation has some latent and strengthening influence on my
Grandson's Configuration; though I own that I have no grounds for
thinking so. At all events I am not alone in my way of extricating
myself from this dilemma; for I find that many of the highest
Circles, sitting as Judges in law courts, use praise and blame
towards Regular and Irregular Figures; and in their homes I know by
experience that, when scolding their children, they speak about
"right" or "wrong" as vehemently and passionately
as if they believed that these names represented real existences, and
that a human Figure is really capable of choosing between them.

Constantly
carrying out their policy of making Configuration the leading idea in
every mind, the Circles reverse the nature of that Commandment which
in Spaceland regulates the relations between parents and children.
With you, children are taught to honour their parents; with us - next
to the Circles, who are the chief object of universal homage - a man
is taught to honour his Grandson, if he has one; or, if not, his Son.
By "honour," however, is by no means meant
"indulgence," but a reverent regard for their highest
interests: and the Circles teach that the duty of fathers is to
subordinate their own interests to those of posterity, thereby
advancing the welfare of the whole State as well as that of their own
immediate descendants.

The weak point
in the system of the Circles - if a humble Square may venture to
speak of anything Circular as containing any element of weakness -
appears to me to be found in their relations with Women.

As it is of the
utmost importance for Society that Irregular births should be
discouraged, it follows that no Woman who has any Irregularities in
her ancestry is a fit partner for one who desires that his posterity
should rise by regular degrees in the social scale.

Now the
Irregularity of a Male is a matter of measurement; but as all Women
are straight, and therefore visibly Regular so to speak, one has to
devise some other means of ascertaining what I may call their
invisible Irregularity, that is to say their potential Irregularities
as regards possible offspring. This is effected by carefully-kept
pedigrees, which are preserved and supervised by the State; and
without a certified pedigree no Woman is allowed to marry.

Now it might
have been supposed that a Circle - proud of his ancestry and
regardful for a posterity which might possibly issue hereafter in a
Chief Circle - would be more careful than any other to choose a wife
who had no blot on her escutcheon. But it is not so. The care in
choosing a Regular wife appears to diminish as one rises in the
social scale. Nothing would induce an aspiring Isosceles, who had
hopes of generating an Equilateral Son, to take a wife who reckoned a
single Irregularity among her Ancestors; a Square or Pentagon, who is
confident that his family is steadily on the rise, does not inquire
above the five-hundredth generation; a Hexagon or Dodecagon is even
more careless of the wife's pedigree; but a Circle has been known
deliberately to take a wife who has had an Irregular Great-
Grandfather, and all because of some slight superiority of lustre, or
because of the charms of a low voice - which, with us, even more than
you, is thought "an excellent thing in Woman."

Such ill-judged
marriages are, as might be expected, barren, if they do not result in
positive Irregularity or in diminution of sides; but none of these
evils have hitherto proved sufficiently deterrent. The loss of a few
sides in a highly-developed Polygon is not easily noticed, and is
sometimes compensated by a successful operation in the
Neo-Therapeutic Gymnasium, as I have described above; and the Circles
are too much disposed to acquiesce in infecundity as a Law of the
superior development. Yet, if this evil be not arrested, the gradual
diminution of the Circular class may soon become more rapid, and the
time may be not far distant when, the race being no longer able to
produce a Chief Circle, the Constitution of Flatland must fall.

One other word
of warning suggests itself to me, though I cannot so easily mention a
remedy; and this also refers to our relations with Women. About three
hundred years ago, it was decreed by the Chief Circle that, since
women are deficient in Reason but abundant in Emotion, they ought no
longer to be treated as rational, nor receive any mental education.
The consequence was that they were no longer. taught to read, nor
even to master Arithmetic enough to enable them to count the angles
of their husband or children; and hence they sensibly declined during
each generation in intellectual power. And this system of female
non-education or quietism still prevails.

My fear is
that, with the best intentions, this policy has been carried so far
as to react injuriously on the Male Sex.

For the
consequence is that, as things now are, we Males have to lead a kind
of bi-lingual, and I may almost say bi-mental, existence. With Women,
we speak of "love," "duty," "right,"
"wrong," "pity," "hope," and other
irrational and emotional conceptions, which have no existence, and
the fiction of which has no object except to control feminine
exuberances; but among ourselves, and in our books, we have an
entirely different vocabulary and I may almost say, idiom.
"Love" then becomes "the anticipation of
benefits"; "duty" becomes "necessity" or
"fitness"; and other words are correspondingly transmuted.
Moreover, among Women, we use language implying the utmost deference
for their Sex; and they fully believe that the Chief Circle Himself
is not more devoutly adored by us than they are: but behind their
backs they are both regarded and spoken of - by all except the very
young - as being little better than "mindless organisms."

Our Theology
also in the Women's chambers is entirely different from our Theology elsewhere.

Now my humble
fear is that this double training, in language as well as in thought,
imposes somewhat too heavy a burden upon the young, especially when,
at the age of three years old, they are taken from the maternal care
and taught to unlearn the old language - except for the purpose of
repeating it in the presence of their Mothers and Nurses-and to learn
the vocabulary and idiom of science. Already methinks I discern a
weakness in the grasp of mathematical truth at the present time as
compared with the more robust intellect of our ancestors three
hundred years ago. I say nothing of the possible danger if a Woman
should ever surreptitiously learn to read and convey to her Sex the
result of her perusal of a single popular volume; nor of the
possibility that the indiscretion or disobedience of some infant Male
might reveal to a Mother the secrets of the logical dialect. On the
simple ground of the enfeebling of the Male intellect, I rest this
humble appeal to the highest Authorities to reconsider the
regulations of Female education.

Part II: OTHER WORLDS

"O brave
new worlds, that have such people in them!"

13. How I had a
Vision of Lineland

IT WAS the last
day but one of the 1999th year of our era, and the first day of the
Long Vacation. Having amused myself till a late hour with my
favourite recreation of Geometry, I had retired to rest with an
unsolved problem in my mind. In the night I had a dream. I saw before
me a vast multitude of small Straight Lines (which I naturally
assumed to be Women) interspersed with other Beings still smaller and
of the nature of lustrous points - all moving to and fro in one and
the same Straight Line, and, as nearly as I could judge, with the
same velocity.

A noise of
confused, multitudinous chirping or twittering issued from them at
intervals as long as they were moving; but sometimes they ceased from
motion, and then all was silence.

Approaching one
of the largest of what I thought to be Women, I accosted her, but
received no answer. A second and a third appeal on my part were
equally ineffectual. Losing patience at what appeared to me
intolerable rudeness, I brought my mouth into a position full in
front of her mouth so as to intercept her motion, and loudly repeated
my question, "Woman, what signifies this concourse, and this
strange and confused chirping, and this monotonous motion to and fro
in one and the same Straight Line?"

"I am no
Woman," replied the small Line: "I am the Monarch of the
world. But thou, whence intrudest thou into my realm of
Lineland?" Receiving this abrupt reply, I begged pardon if I had
in any way startled or molested his Royal Highness; and describing
myself as a stranger I besought the King to give me some account of
his dominions. But I had the greatest possible difficulty in
obtaining any information on points that really interested me; for
the Monarch could not refrain from constantly assuming that whatever
was familiar to him must also be known to me and that I was
simulating ignorance in jest. However, by persevering questions I
elicited the following facts:

It seemed that
this poor ignorant Monarch - as he called himself - was persuaded
that the Straight Line which he called his Kingdom, and in which he
passed his existence, constituted the whole of the world, and indeed
the whole of Space. Not being able either to move or to see, save in
his Straight Line, he had no conception of anything out of it. Though
he had heard my voice when I first addressed him, the sounds had come
to him in a manner so contrary to his experience that he had made no
answer, "seeing no man," as he expressed it, "and
hearing a voice as it were from my own intestines." Until the
moment when I placed my mouth in his World, he had neither seen me,
nor heard anything except confused sounds beating against - what I
called his side, but what he called his inside or stomach; nor had he
even now the least conception of the region from which I had come.
Outside his World, or Line, all was a blank to him; nay, not even a
blank, for a blank implies Space; say, rather, all was non existent.

His subjects -
of whom the small Lines were men and the Points Women - were all
alike confined in motion and eye-sight to that single Straight Line,
which was their World. It need scarcely be added that the whole of
their horizon was limited to a Point; nor would any one ever see
anything but a Point. Man, woman, child, thing - each was a Point to
the eye of a Linelander. Only by the sound of the voice could sex or
age be distinguished. Moreover, as each individual occupied the whole
of the narrow path, so to speak, which constituted his Universe, and
no one could move to the right or left to make way for passers by, it
followed that no Linelander could ever pass another. Once neighbours,
always neighbours. Neighbourhood with them was like marriage with us.
Neighbours remained neighbours,till death did them part.

Such a life,
with all vision limited to a Point, and all motion to a Straight
Line, seemed to me inexpressibly dreary; and I was surprised to note
the vivacity and cheerfulness of the King. Wondering whether it was
possible, amid circumstances so unfavourable to domestic relations,
to enjoy the pleasures of conjugal union, I hesitated for some time
to question his Royal Highness on so delicate a subject; but at last
I plunged into it by abruptly inquiring as to the health of his
family. "My wives and children," he replied, "are well
and happy."

Staggered at
this answer - for in the immediate proximity of the Monarch (as I had
noted in my dream before I entered Lineland) there were none but Men
- I ventured to reply, "Pardon me, but I cannot imagine how your
Royal Highness can at any time either see or approach their
Majesties, when there are at least half a dozen intervening
individuals, whom you can neither see through, nor pass by? Is it
possible that in Lineland proximity is not necessary for marriage and
for the generation of children?"

"How can
you ask so absurd a question?" replied the Monarch. "If it
were indeed as you suggest, the Universe would soon be depopulated.
No, no; neigbourhood is needless for the union of hearts; and the
birth of children is too important a matter to have been allowed to
depend upon such an accident as proximity. You cannot be ignorant of
this. Yet since you are pleased to affect ignorance, I will instruct
you as if you were the veriest baby in Lineland. Know, then, that
marriages are consummated by means of the faculty of sound and the
sense of hearing.

"You are
of course aware that every Man has two mouths or voices - as well as
two eyes - a bass at one and a tenor at the other of his extremities.
I should not mention this, but that I have been unable to distinguish
your tenor in the course of our conversation." I replied that I
had but one voice, and that I had not been aware that his Royal
Highness had two. "That confirms my impression," said the
King, "that you are not a Man, but a feminine Monstrosity with a
bass voice, and an utterly uneducated ear. But to continue.

"Nature
having herself ordained that every Man should wed two wives - "
"Why two?" asked I. "You carry your affected
simplicity too far," he cried. "How can there be a
completely harmonious union without the combination of the Four in
One, viz. the Bass and Tenor of the Man and the Soprano and Contralto
of the two Women?" "But supposing," said I, "that
a man should prefer one wife or three?" "It is
impossible," he said; "it is as inconceivable as that two
and one should make five, or that the human eye should see a Straight
Line." I would have interrupted him; but he proceeded as follows:

"Once in
the middle of each week a Law of Nature compels us to move to and fro
with a rhythmic motion of more than usual violence, which continues
for the time you would take to count a hundred and one. In the midst
of this choral dance, at the fifty-first pulsation, the inhabitants
of the Universe pause in full career, and each individual sends forth
his richest, fullest, sweetest strain. It is in this decisive moment
that all our marriages are made. So exquisite is the adaptation of
Bass to Treble, of Tenor to Contralto, that oftentimes the Loved
Ones, though twenty thousand leagues away, recognize at once the
responsive note of their destined Lover; and, penetrating the paltry
obstacles of distance, Love unites the three. The marriage in that
instant consummated results in a threefold Male and Female offspring
which takes its place in Lineland."

"What!
Always threefold?" said I. "Must one wife then always have twins?"

"Bass-voiced
Monstrosity! yes," replied the King. "How else could the
balance of the Sexes be maintained, if two girls were not born for
every boy? Would you ignore the very Alphabet of Nature?" He
ceased, speechless for fury; and some time elasped before I could
induce him to resume his narrative.

"You will
not, of course, suppose that every bachelor among us finds his mates
at the first wooing in this universal Marriage Chorus. On the
contrary, the process is by most of us many times repeated. Few are
the hearts whose happy lot it is at once to recognize in each other's
voices the partner intended for them by Providence, and to fly into a
reciprocal and perfectly harmonious embrace. With most of us the
courtship is of long duration. The Wooer's voices may perhaps accord
with one of the future wives, but not with both; or not, at first,
with either; or the Soprano and Contralto may not quite harmonize. In
such cases Nature has provided that every weekly Chorus shall bring
the three Lovers into closer harmony. Each trial of voice, each fresh
discovery of discord, almost imperceptibly induces the less perfect
to modify his or her vocal utterance so as to approximate to the more
perfect. And after many trials and many approximations, the result is
at last achieved. There comes a day at last, when, while the wonted
Marriage Chorus goes forth from universal Lineland, the three far-off
Lovers suddenly find themselves in exact harmony, and, before they
are awake, the wedded Triplet is rapt vocally into a duplicate
embrace; and Nature rejoices over one more marriage and over three
more births."

14. How I
vainly tried to explain the nature of Flatland

THINKING THAT
it was time to bring down the Monarch from his raptures to the level
of common sense, I determined to endeavour to open up to him some
glimpses of the truth, that is to say of the nature of things in
Flatland. So I began thus: "How does your Royal Highness
distinguish the shapes and positions of his subjects? I for my part
noticed by the sense of sight, before I entered your Kingdom, that
some of your people are Lines and others Points, and that some of the
Lines are larger - " "You speak of an impossibility,"
interrupted the King; "you must have seen a vision; for to
detect the difference between a Line and a Point by the sense of
sight is, as every one knows, in the nature of things, impossible;
but it can be detected by the sense of hearing, and by the same means
my shape can be exactly ascertained. Behold me - I am a Line, the
longest in Lineland, over six inches of Space - " "Of
Length," I ventured to suggest. "Fool," said he,
"Space is Length. Interrupt me again, and I have done."

I apologized;
but he continued scornfully, "Since you are impervious to
argument, you shall hear with your ears how by means of my two voices
I reveal my shape to my Wives, who are at this moment six thousand
miles seventy yards two feet eight inches away, the one to the North,
the other to the South. Listen, I call to them."

He chirruped,
and then complacently continued: "My wives at this moment
receiving the sound of one of my voices, closely followed by the
other, and perceiving that the latter reaches them after an interval
in which sound can traverse 6.457 inches, infer that one of my mouths
is 6.457 inches further from them than the other, and accordingly
know my shape to be 6.457 inches. But you will of course understand
that my wives do not make this calculation every time they hear my
two voices. They made it, once for all, before we were married. But
they could make it at any time. And in the same way I can estimate
the shape of any of my Male subjects by the sense of sound."

"But
how," said I, "if a Man feigns a Woman's voice with one of
his two voices, or so disguises his Southern voice that it cannot be
recognized as the echo of the Northern? May not such deceptions cause
great inconvenience? And have you no means of checking frauds of this
kind by commanding your neighbouring subjects to feel one
another?" This of course was a very stupid question, for feeling
could not have answered the purpose; but I asked with the view of
irritating the Monarch, and I succeeded perfectly.

"What!"
cried he in horror, "explain your meaning." "Feel,
touch, come into contact," I replied. "If you mean by
feeling," said the King, "approaching so close as to leave
no space between two individuals, know, Stranger, that this offence
is punishable in my dominions by death. And the reason is obvious.
The frail form of a Woman, being liable to be shattered by such an
approximation, must be preserved by the State; but since Women cannot
be distinguished by the sense of sight from Men, the Law ordains
universally that neither Man nor Woman shall be approached so closely
as to destroy the interval between the approximator and the approximated.

"And
indeed what possible purpose would be served by this illegal and
unnatural excess of approximation which you call touching, when all
the ends of so brutal and coarse a process are attained at once more
easily and more exactly by the sense of hearing? As to your suggested
danger of deception, it is non-existent: for the Voice, being the
essence of one's Being, cannot be thus changed at will. But come,
suppose that I had the power of passing through solid things, so that
I could penetrate my subjects, one after another, even to the number
of a billion, verifying the size and distance of each by the sense of
feeling: how much time and energy would be wasted in this clumsy and
inaccurate method! Whereas now, in one moment of audition, I take as
it were the census and statistics, local, corporeal, mental and
spiritual, of every living being in Lineland. Hark, only hark!"

So saying he
paused and listened, as if in an ecstasy, to a sound which seemed to
me no better than a tiny chirping from an innumerable multitude of
lilliputian grasshoppers.

"Truly,"
replied I, "your sense of hearing serves you in good stead, and
fills up many of your deficiencies. But permit me to point out that
your life in Lineland must be deplorably dull. To see nothing but a
Point! Not even to be able to contemplate a Straight Line! Nay, not
even to know what a Straight Line isl To see, yet be cut off from
those Linear prospects which are vouchsafed to us in Flatland! Better
surely to have no sense of sight at all than to see so little! I
grant you I have not your discriminative faculty of hearing; for the
concert of all Lineland which gives you such intense pleasure, is to
me no better than a multitudinous twittering or chirping. But at
least I can discern, by sight, a Line from a Point. And let me prove
it. Just before I came into your kingdom, I saw you dancing from left
to right, and then from right to left, with Seven Men and a Woman in
your immediate proximity on the left, and eight Men and two Women on
your right. Is not this correct?"

"It is
correct," said the King, "so far as the numbers and sexes
are concerned, though I know not what you mean by 'right' and 'left.'
But I deny that you saw these things. For how could you see the Line,
that is to say the inside, of any Man? But you must have heard these
things, and then dreamed that you saw them. And let me ask what you
mean by those words 'left' and 'right.' I suppose it is your way of
saying Northward and Southward."

"Not
so," replied I; "besides your motion of Northward and
Southward, there is another motion which I call from right to
left." King. Exhibit to me, if you please, this motion from left
to right. I. Nay, that I cannot do, unless you could step out of your
Line altogether.

King. Out of my
Line? Do you mean out of the world? Out of Space?

I. Well, yes.
Out of your World. Out of your Space. For your Space is not the true
Space. True Space is a Plane; but your Space is only a Line.

King. If you
cannot indicate this motion from left to right by yourself moving in
it, then I beg you to describe it to me in words.

I. If you
cannot tell your right side from your left, I fear that no words of
mine can make my meaning clear to you. But surely you cannot be
ignorant of so simple a distinction.

King. I do not
in the least understand you.

I. Alas! How
shall I make it clear? When you move straight on, does it not
sometimes occur to you that you could move in some other way, turning
your eye round so as to look in the direction towards which your side
is now fronting? In other words, instead of always moving in the
direction of one of your extremities, do you never feel a desire to
move in the direction, so to speak, of your side?

King. Never.
And what do you mean? How can a man's inside "front" in any
direction? Or how can a man move in the direction of his inside?

I. Well then,
since words cannot explain the matter, I will try deeds, and will
move gradually out of Lineland in the direction which I desire to
indicate to you.

At the word I
began to move my body out of Lineland. As long as any part of me
remained in his dominion and in his view, the King kept exclaiming,
"I see you, I see you still; you are not moving." But when
I had at last moved myself out of his Line, he cried in his shrillest
voice, "She is vanished; she is dead." "I am not
dead," replied I; "I am simply out of Lineland, that is to
say, out of the Straight Line which you call Space, and in the true
Space, where I can see things as they are. And at this moment I can
see your Line, or side - or inside as you are pleased to call it; and
I can see also the Men and Women on the North and South of you, whom
I will now enumerate, describing their order, their size, and the
interval between each."

When I had done
this at great length, I cried triumphantly, "Does that at last
convince you?" And, with that, I once more entered Lineland,
taking up the same position as before.

But the Monarch
replied, "If you were a Man of sense - though, as you appear to
have only one voice I have little doubt you are not a Man but a Woman
- but, if you had a particle of sense, you would listen to reason.
You ask me to believe that there is another Line besides that which
my senses indicate, and another motion besides that of which I am
daily conscious. I, in return, ask you to describe in words or
indicate by motion that other Line of which you speak. Instead of
moving, you merely exercise some magic art of vanishing and returning
to sight; and instead of any lucid description of your new World, you
simply tell me the numbers and sizes of some forty of my retinue,
facts known to any child in my capital. Can anything be more
irrational or audacious? Acknowledge your folly or depart from my dominions."

Furious at his
perversity, and especially indignant that he professed to be ignorant
of my sex, I retorted in no measured terms, "Besotted Being! You
think yourself the perfection of existence, while you are in reality
the most imperfect and imbecile. You profess to see, whereas you can
see nothing but a Point! You plume yourself on inferring the
existence of a Straight Line; but I can see Straight Lines, and infer
the existence of Angles, Triangles, Squares, Pentagons, Hexagons, and
even Circles. Why waste more words? Suffice it that I am the
completion of your incomplete self. You are a Line, but I am a Line
of Lines, called in my country a Square: and even I, infinitely
superior though I am to you, am of little account among the great
nobles of Flatland, whence I have come to visit you, in the hope of
enlightening your ignorance."

Hearing these
words the King advanced towards me with a menacing cry as if to
pierce me through the diagonal; and in that same moment there arose
from myriads of his subjects a multitudinous war-cry, increasing in
vehemence till at last methought it rivalled the roar of an army of a
hundred thousand Isosceles, and the artillery of a thousand
Pentagons. Spell-bound and motionless, I could neither speak nor move
to avert the impending destruction; and still the noise grew louder,
and the King came closer, when I awoke to find the breakfast-bell
recalling me to the realities of Flatland.

15. Concerning
a Stranger from Spaceland

FROM DREAMS I
proceed to facts.

It was the last
day of the 1999th year of our era. The pattering of the rain had long
ago announced nightfall; and I was sitting4 in the company of my
wife, musing on the events of the past and the prospects of the
coming year, the coming century, the coming Millennium.

My four Sons
and two orphan Grandchildren had retired to their several apartments;
and my wife alone remained with me to see the old Millennium out and
the new one in. I was rapt in thought, pondering in my mind some
words that had casually issued from the mouth of my youngest
Grandson, a most promising young Hexagon of unusual brilliancy and
perfect angularity. His uncles and I had been giving him his usual
practical lesson in Sight Recognition, turning ourselves upon our
centres, now rapidly, now more slowly, and questioning him as to our
positions; and his answers had been so satisfactory that I had been
induced to reward him by giving him a few hints on Arithmetic, as
applied to Geometry.

Taking nine
Squares, each an inch every way, I had put them together so as to
make one large Square, with a side of three inches, and I had hence
proved to my little Grandson that - though it was impossible for us
to see the inside of the Square - yet we might ascertain the number
of square inches in a Square by simply squaring the number of inches
in the side: "and thus," said I, "we know that 32, or
9, represents the number of square inches in a Square whose side is 3
inches long."

The little
Hexagon meditated on this a while and then said to me; "But you
have been teaching me to raise numbers to the third power: I suppose
33 must mean something in Geometry; what does it mean?"
"Nothing at all," replied I, "not at least in
Geometry; for Geometry has only Two Dimensions." And then I
began to shew the boy how a Point by moving through a length of three
inches makes a Line of three inches, which may be represented by 3;
and how a Line of three inches, moving parallel to itself through a
length of three inches, makes a Square of three inches every way,
which may be represented by 32.

Upon this, my
Grandson, again returning to his former suggestion, took me up rather
suddenly and exclaimed, "Well, then, if a Point by moving three
inches, makes a Line of three inches represented by 3; and if a
straight Line of three inches, moving parallel to itself, makes a
Square of three inches every way, represented by 32; it must be that
a Square of three inches every way, moving somehow parallel to itself
(but I don't see how) must make Something else (but I don't see what)
of three inches every way - and this must be represented by 33."

"Go to
bed," said I, a little ruffled by this interruption: "if
you would talk less nonsense, you would remember more sense."

So my Grandson
had disappeared in disgrace; and there I sat by my Wife's side,
endeavouring to form a retrospect of the year 1999 and of the
possibilities of the year 2000, but not quite able to shake off the
thoughts suggested by the prattle of my bright little Hexagon. Only a
few sands now remained in the half-hour glass. Rousing myself from my
reverie I turned the glass Northward for the last time in the old
Millennium; and in the act, I exclaimed aloud, "The boy is a fool."

Straightway I
became conscious of a Presence in the room, and a chilling breath
thrilled through my very being. "He is no such thing,"
cried my Wife, "and you are breaking the Commandments in thus
dishonouring your own Grandson." But I took no notice of her.
Looking round in every direction I could see nothing; yet still I
felt a Presence, and shivered as the cold whisper came again. I
started up. "What is the matter?" said my Wife, "there
is no draught; what are you looking for? There is nothing."
There was nothing; and I resumed my seat, again exclaiming, "The
boy is a fool, I say; 33 can have no meaning in Geometry." At
once there came a distinctly audible reply, "The boy is not a
fool; and 33 has an obvious Geometrical meaning."

My Wife as well
as myself heard the words, although she did not understand their
meaning, and both of us sprang forward in the direction of the sound.
What was our horror when we saw before us a Figure! At the first
glance it appeared to be a Woman, seen sideways; but a moment's
observation shewed me that the extremities passed into dimness too
rapidly to represent one of the Female Sex; and I should have thought
it a Circle, only that it seemed to change its size in a manner
impossible for a Circle or for any regular Figure of which I had had experience.

But my Wife had
not my experience, nor the coolness necessary to note these
characteristics. With the usual hastiness and unreasoning jealousy of
her Sex, she flew at once to the conclusion that a Woman had entered
the house through some small aperture. "How comes this person
here?" she exclaimed, "you promised me, my dear, that there
should be no ventilators in our new house." "Nor are there
any," said I; "but what makes you think that the stranger
is a Woman? I see by my power of Sight Recognition - " "Oh,
I have no patience with your Sight Recognition," replied she,
"Feeling is believing' and A Straight Line to the touch is worth
a Circle to the sight'" - two Proverbs, very common with the
Frailer Sex in Flatland.

"Well,"
said I, for I was afraid of irritating her, "if it must be so,
demand an introduction." Assuming her most gracious manner, my
Wife advanced towards the Stranger, "Permit me, Madam, to feel
and be felt by - - " then, suddenly recoiling, "Oh! it is
not a Woman, and there are no angles either, not a trace of one. Can
it be that I have so misbehaved to a perfect Circle?"

"I am
indeed, in a certain sense a Circle," replied the Voice,
"and a more perfect Circle than any in Flatland, but to speak
more accurately, I am many Circles in one." Then he added more
mildly, "I have a message, dear Madam, to your husband, which I
must not deliver in your presence; and, if you would suffer us to
retire for a few minutes - - " But my Wife would not listen to
the proposal that our august Visitor should so incommode himself, and
assuring the Circle that the hour of her own retirement had long
passed, with many reiterated apologies for her recent indiscretion,
she at last retreated to her apartment.

I glanced at
the half-hour glass. The last sands had fallen. The third Millennium
had begun.

16. How the
Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland

AS SOON as the
sound of the Peace-cry of my departing Wife had died away, I began to
approach the Stranger with the intention of taking a nearer view and
of bidding him be seated: but his appearance struck me dumb and
motionless with astonishment. Without the slightest symptoms of
angularity he nevertheless varied every instant with gradations of
size and brightness scarcely possible for any Figure within the scope
of my experience. The thought flashed across me that I might have
before me a burglar or cut- throat, some monstrous Irregular
Isosceles, who, by feigning the voice of a Circle, had obtained
admission somehow into the house, and was now preparing to stab me
with his acute angle.

In a
sitting-room, the absence of Fog (and the season happened to be
remarkably dry), made it difficult for me to trust to Sight
Recognition, especially at the short distance at which I was
standing. Desperate with fear, I rushed forward with an
unceremonious, "You must permit me, Sir - " and felt him.
My Wife was right. There was not the trace of an angle, not the
slightest roughness or inequality: never in my life had I met with a
more perfect Circle. He remained motionless while I walked round him,
beginning from his eye and returning to it again. Circular he was
throughout, a perfectly satisfactory Circle; there could not be a
doubt of it. Then followed a dialogue, which I will endeavour to set
down as near as I can recollect it, omitting only some of my profuse
apologies - for I was covered with shame and humiliation that I, a
Square, should have been guilty of the impertinence of feeling a
Circle. It was commenced by the Stranger with some impatience at the
lengthiness of my introductory process.

Stranger. Have
you felt me enough by this time? Are you not introduced to me yet?

I. Most
illustrious Sir, excuse my awkwardness, which arises not from
ignorance of the usages of polite society, but from a little surprise
and nervousness, consequent on this somewhat unexpected visit. And I
beseech you to reveal my indiscretion to no one, and especially not
to my Wife. But before your Lordship enters into further
communications, would he deign to satisfy the curiosity of one who
would gladly know whence his Visitor came?

Stranger. From
Space, from Space, Sir: whence else?

I. Pardon me,
my Lord, but is not your Lordship already in Space, your Lordship and
his humble servant, even at this moment?

Stranger. Pooh!
what do you know of Space? Define Space.

I. Space, my
Lord, is height and breadth indefinitely prolonged. Stranger.
Exactly: you see you do not even know what Space is. You think it is
of Two Dimensions only; but I have come to announce to you a Third -
height, breadth, and length.

I. Your
Lordship is pleased to be merry. We also speak of length and height,
or breadth and thickness, thus denoting Two Dimensions by four names.

Stranger. But I
mean not only three names, but Three Dimensions.

I. Would your
Lordship indicate or explain to me in what direction is the Third
Dimension, unknown to me?

Stranger. I
came from it. It is up above and down below.

I. My Lord
means seemingly that it is Northward and Southward.

Stranger. I
mean nothing of the kind. I mean a direction in which you cannot
look, because you have no eye in your side.

I. Pardon me,
my Lord, a moment's inspection will convince your Lordship that I
have a perfect luminary at the juncture of two of my sides.

Stranger. Yes:
but in order to see into Space you ought to have an eye, not on your
Perimeter, but on your side, that is, on what you would probably call
your inside; but we in Spaceland should call it your side.

I. An eye in my
inside! An eye in my stomach! Your Lordship Jests.

Stranger. I am
in no jesting humour. I tell you that I come from Space, or, since
you will not understand what Space means, from the Land of Three
Dimensions whence I but lately looked down upon your Plane which you
call Space forsooth. From that position of advantage I discerned all
that you speak of as solid (by which you mean "enclosed on four
sides"), your houses, your churches, your very chests and safes,
yes even your insides and stomachs, all lying open and exposed to my view.

I. Such
assertions are easily made, my Lord.

Stranger. But
not easily proved, you mean. But I mean to prove mine. When I
descended here, I saw your four Sons, the Pentagons, each in his
apartment, and your two Grandsons the Hexagons; I saw your youngest
Hexagon remain a while with you and then retire to his room, leaving
you and your Wife alone. I saw your Isosceles servants, three in
number, in the kitchen at supper, and the little Page in the
scullery. Then I came here, and how do you think I came?

I. Through the
roof, I suppose.

Stranger. Not
so. Your roof, as you know very well, has been recently repaired, and
has no aperture by which even a Woman could penetrate. I tell you I
come from Space. Are you not convinced by what I have told you of
your children and household?

I. Your
Lordship must be aware that such facts touching the belongings of his
humble servant might be easily ascertained by any one in the
neighbourhood possessing your Lordship's ample means of obtaining information.

Stranger. (To
himself.) What must I do? Stay; one more argument suggests itself to
me. When you see a Straight Line - your wife, for example - how many
Dimensions do you attribute to her?

I. Your
Lordship would treat me as if I were one of the vulgar who, being
ignorant of Mathematics, suppose that a Woman is really a Straight
Line, and only of One Dimension. No, no, my Lord; we Squares are
better advised, and are as well aware as your Lordship that a Woman,
though popularly called a Straight Line, is, really and
scientifically, a very thin Parallelogram, possessing Two Dimensions,
like the rest of us, viz., length and breadth (or thickness).

Stranger. But
the very fact that a Line is visible implies that it possesses yet
another Dimension.

I. My Lord, I
have just acknowledged that a Woman is broad as well as long. We see
her length, we infer her breadth; which, though very slight, is
capable of measurement.

Stranger. You
do not understand me. I mean that when you see a Woman, you ought -
besides inferring her breadth - to see her length, and to see what we
call her height; although that last Dimension is infinitesimal in
your country. If a Line were mere length without "height,"
it would cease to occupy Space and would become invisible. Surely you
must recognize this?

I. I must
indeed confess that I do not in the least understand your Lordship.
When we in Flatland see a Line, we see length and brightness. If the
brightness disappears, the Line is extinguished, and, as you say,
ceases to occupy Space. But am I to suppose that your Lordship gives
to brightness the title of a Dimension, and that what we call
"bright" you call "high"?

Stranger. No,
indeed. By "height" I mean a Dimension like your length:
only, with you, "height" is not so easily perceptible,
being extremely small.

I. My Lord,
your assertion is easily put to the test. You say I have a Third
Dimension, which you call "height." Now, Dimension implies
direction and measurement. Do but measure my "height," or
merely indicate to me the direction in which my "height"
extends, and I will become your convert. Otherwise, your Lordship's
own understanding must hold me excused.

Stranger. (To
himself.) I can do neither. How shall I convince him? Surely a plain
statement of facts followed by ocular demonstration ought to suffice.
- Now, Sir; listen to me.

You are living
on a Plane. What you style Flatland is the vast level surface of what
I may call a fluid, on, or in, the top of which you and your
countrymen move about, without rising above it or falling below it.

I am not a
plane Figure, but a Solid. You call me a Circle; but in reality I am
not a Circle, but an infinite number of Circles, of size varying from
a Point to a Circle of thirteen inches in diameter, one placed on the
top of the other. When I cut through your plane as I am now doing, I
make in your plane a section which you, very rightly, call a Circle.
For even a Sphere - which is my proper name in my own country - if he
manifest himself at all to an inhabitant of Flatland - must needs
manifest himself as a Circle.

Do you not
remember - for I, who see all things, discerned last night the
phantasmal vision of Lineland written upon your brain - do you not
remember, I say, how, when you entered the realm of Lineland, you
were compelled to manifest yourself to the King, not as a Square, but
as a Line, because that Linear Realm had not Dimensions enough to
represent the whole of you, but only a slice or section of you? In
precisely the same way, your country of Two Dimensions is not
spacious enough to represent me, a being of Three, but can only
exhibit a slice or section of me, which is what you call a Circle.

The diminished
brightness of your eye indicates incredulity. But now prepare to
receive proof positive of the truth of my assertions. You cannot
indeed see more than one of my sections, or Circles, at a time; for
you have no power to raise your eye out of the plane of Flatland; but
you can at least see that, as I rise in Space, so my sections become
smaller. See now, I will rise; and the effect upon your eye will be
that my Circle will become smaller and smaller till it dwindles to a
point and finally vanishes.

There was no
"rising" that I could see; but he diminished and finally
vanished. I winked once or twice to make sure that I was not
dreaming. But it was no dream. For from the depths of nowhere came
forth a hollow voice - close to my heart it seemed - "Am I quite
gone? Are you convinced now? Well, now I will gradually return to
Flatland and you shall see my section become larger and larger."

Every reader in
Spaceland will easily understand that my mysterious Guest was
speaking the language of truth and even of simplicity. But to me,
proficient though I was in Flatland Mathematics, it was by no means a
simple matter. The rough diagram given above will make it clear to
any Spaceland child that the Sphere, ascending in the three positions
indicated there, must needs have manifested himself to me, or to any
Flatlander, as a Circle, at first of full size, then small, and at
last very small indeed, approaching to a Point. But to me, although I
saw the facts before me, the causes were as dark as ever. All that I
could comprehend was, that the Circle had made himself smaller and
vanished, and that he had now reappeared and was rapidly making
himself larger.

When he
regained his original size, he heaved a deep sigh; for he perceived
by my silence that I had altogether failed to comprehend him. And
indeed I was now inclining to the belief that he must be no Circle at
all, but some extremely clever juggler; or else that the old wives'
tales were true, and that after all there were such people as
Enchanters and Magicians.

After a long
pause he muttered to himself, "One resource alone remains, if I
am not to resort to action. I must try the method of Analogy."
Then followed a still longer silence, after which he continued our dialogue.

Sphere. Tell
me, Mr. Mathematician; if a Point moves Northward, and leaves a
luminous wake, what name would you give to the wake?

I. A straight Line.

Sphere. And a
straight Line has how many extremities?

I. Two.

Sphere. Now
conceive the Northward straight Line moving parallel to itself, East
and West, so that every point in it leaves behind it the wake of a
straight Line. What name will you give to the Figure thereby formed?
We will suppose that it moves through a distance equal to the
original straight Line. - What name, I say?

I. A Square.

Sphere. And how
many sides has a Square? How many angles?

I. Four sides
and four angles.

Sphere. Now
stretch your imagination a little, and conceive a Square in Flatland,
moving parallel to itself upward.

I. What? Northward?

Sphere. No, not
Northward; upward; out of Flatland altogether.

If it moved
Northward, the Southern points in the Square would have to move
through the positions previously occupied by the Northern points. But
that is not my meaning.

I mean that
every Point in you - for you are a Square and will serve the purpose
of my illustration - every Point in you, that is to say in what you
call your inside, is to pass upwards through Space in such a way that
no Point shall pass through the position previously occupied by any
other Point; but each Point shall describe a straight Line of its
own. This is all in accordance with Analogy; surely it must be clear
to you.

Restraining my
impatience - for I was now under a strong temptation to rush blindly
at my Visitor and to precipitate him into Space, or out of Flatland,
anywhere, so that I could get rid of him - I replied: -

"And what
may be the nature of the Figure which I am to shape out by this
motion which you are pleased to denote by the word 'upward'? I
presume it is describable in the language of Flatland . "

Sphere. Oh,
certainly. It is all plain and simple, and in strict accordance with
Analogy - only, by the way, you must not speak of the result as being
a Figure, but as a Solid. But I will describe it to you. Or rather
not I, but Analogy.

We began with a
single Point, which of course - being itself a Point - has only one
terminal Point.

One Point
produces a Line with two terminal Points.

One Line
produces a Square with four terminal Points.

Now you can
give yourself the answer to your own question: 1, 2. 4, are evidently
in Geometrical Progression. What is the next number?

I. Eight.

Sphere.
Exactly. The one Square produces a Something-which- you-do-not-as-yet-know-a-name-for-But-which-we-call-a-Cube
with eight terminal Points. Now are you convinced?

I. And has this
Creature sides, as well as angles or what you call "terminal Points"?

Sphere. Of
course; and all according to Analogy. But, by the way, not what you
call sides, but what we call sides. You would call them solids.

I. And how many
solids or sides will appertain to this Being whom I am to generate by
the motion of my inside in an "upward" direction, and whom
you call a Cube?

Sphere. How can
you ask? And you a mathematician! The side of anything is always, if
I may so say, one Dimension behind the thing. Consequently, as there
is no Dimension behind a Point, a Point has 0 sides; a Line, if I may
say, has 2 sides (for the Points of a line may be called by courtesy,
its sides); a Square has 4 sides; 0, 2, 4; what Progression do you
call that?

I. Arithmetical.

Sphere. And
what is the next number?

I. Six.

Sphere.
Exactly. Then you see you have answered your own question. The Cube
which you will generate will be bounded by six sides, that is to say,
six of your insides. You see it all now, eh?

"Monster,"
I shrieked, "be thou juggler, enchanter, dream, or devil, no
more will I endure thy mockeries. Either thou or I must perish."
And saying these words I precipitated myself upon him.

17. How the
Sphere, having in vain tried words, resorted to deeds

IT WAS in vain.
I brought my hardest right angle into violent collision with the
Stranger, pressing on him with a force sufficient to have destroyed
any ordinary Circle: but I could feel him slowly and unarrestably
slipping from my contact; no edging to the right nor to the left, but
moving somehow out of the world, and vanishing to nothing. Soon there
was a blank. But still I heard the Intruder's voice.

Sphere. Why
will you refuse to listen to reason? I had hoped to find in you - as
being a man of sense and an accomplished mathematician - a fit
apostle for the Gospel of the Three Dimensions, which I am allowed to
preach once only in a thousand years: but now I know not how to
convince you. Stay, I have it. Deeds, and not words, shall proclaim
the truth. Listen, my friend.

I have told you
I can see from my position in Space the inside of all things that you
consider closed. For example, I see in yonder cupboard near which you
are standing, several of what you call boxes (but like everything
else in Flatland, they have no tops nor bottoms) full of money; I see
also two tablets of accounts. I am about to descend into that
cupboard and to bring you one of those tablets. I saw you lock the
cupboard half an hour ago, and I know you have the key in your
possession. But I descend from Space; the doors, you see, remain
unmoved. Now I am in the cupboard and am taking the tablet. Now I
have it. Now I ascend with it.

I rushed to the
closet and dashed the door open. One of the tablets was gone. With a
mocking laugh, the Stranger appeared in the other corner of the room,
and at the same time the tablet appeared upon the floor. I took it
up. There could be no doubt - it was the missing tablet.

I groaned with
horror, doubting whether I was not out of my senses; but the Stranger
continued: "Surely you must now see that my explanation, and no
other, suits the phenomena. What you call Solid things are really
superficial; what you call Space is really nothing but a great Plane.
I am in Space, and look down upon the insides of the things of which
you only see the outsides. You could leave this Plane yourself, if
you could but summon up the necessary volition. A slight upward or
downward motion would enable you to see all that I can see.

"The
higher I mount, and the further I go from your Plane, the more I can
see, though of course I see it on a smaller scale. For example, I am
ascending; now I can see your neighbour the Hexagon and his family in
their several apartments; now I see the inside of the Theatre, ten
doors off, from which the audience is only just departing; and on the
other side a Circle in his study, sitting at his books. Now I shall
come back to you. And, as a crowning proof, what do you say to my
giving you a touch, just the least touch, in your stomach? It will
not seriously injure you, and the slight pain you may suffer cannot
be compared with the mental benefit you will receive."

Before I could
utter a word of remonstrance, I felt a shooting pain in my inside,
and a demoniacal laugh seemed to issue from within me. A moment
afterwards the sharp agony had ceased, leaving nothing but a dull
ache behind, and the Stranger began to reappear, saying, as he
gradually increased in size, "There, I have not hurt you much,
have I? If you are not convinced now, I don't know what will convince
you. What say you?"

My resolution
was taken. It seemed intolerable that I should endure existence
subject to the arbitrary visitations of a Magician who could thus
play tricks with one's very stomach. If only I could in any way
manage to pin him against the wall till help came!

Once more I
dashed my hardest angle against him, at the same time alarming the
whole household by my cries for aid. I believe, at the moment of my
onset, the Stranger had sunk below our Plane, and really found
difficulty in rising. In any case he remained motionless, while I,
hearing, as I thought, the sound of some help approaching, pressed
against him with redoubled vigour, and continued to shout for assistance.

A convulsive
shudder ran through the Sphere. "This must not be," I
thought I heard him say: "either he must listen to reason, or I
must have recourse to the last resource of civilization." Then,
addressing me in a louder tone, he hurriedly exclaimed, "Listen:
no stranger must witness what you have witnessed. Send your Wife back
at once, before she enters the apartment. The Gospel of Three
Dimensions must not be thus frustrated. Not thus must the fruits of
one thousand years of waiting be thrown away. I hear her coming.
Back! back! Away from me, or you must go with me - whither you know
not - into the Land of Three Dimensions!"

18. How I came
to Spaceland, and what I saw there

AN UNSPEAKABLE
horror seized me. There was a darkness; then a dizzy, sickening
sensation of sight that was not like seeing; I saw a Line that was no
Line; Space that was not Space: I was myself, and not myself. When I
could find voice, I shrieked aloud in agony, "Either this is
madness or it is Hell." "It is neither," calmly
replied the voice of the Sphere, "it is Knowledge; it is Three
Dimensions: open your eye once again and try to look steadily."

I looked, and,
behold, a new world! There stood before me, visibly incorporate, all
that I had before inferred, conjectured, dreamed, of perfect Circular
beauty. What seemed the centre of the Stranger's form lay open to my
view: yet I could see no heart, nor lungs, nor arteries, only a
beautiful harmonious Something - for which I had no words; but you,
my Readers in Spaceland, would call it the surface of the Sphere.

Prostrating
myself mentally before my Guide, I cried, "How is it, O divine
ideal of consummate loveliness and wisdom that I see thy inside, and
yet cannot discern thy heart, thy lungs, thy arteries, thy
liver?" "What you think you see, you see not," he
replied; "it is not given to you, nor to any other Being to
behold my internal parts. I am of a different order of Beings from
those in Flatland. Were I a Circle, you could discern my intestines,
but I am a Being, composed as I told you before, of many Circles, the
Many in the One, called in this country a Sphere. And, just as the
outside of a Cube is a Square, so the outside of a Sphere presents
the appearance of a Circle."

Bewildered
though I was by my Teacher's enigmatic utterance, I no longer chafed
against it, but worshipped him in silent adoration. He continued,
with more mildness in his voice. "Distress not yourself if you
cannot at first understand the deeper mysteries of Spaceland. By
degrees they will dawn upon you. Let us begin by casting back a
glance at the region whence you came. Return with me a while to the
plains of Flatland, and I will shew you that which you have often
reasoned and thought about, but never seen with the sense of sight -
a visible angle." "Impossible!" I cried; but, the
Sphere leading the way, I followed as if in a dream, till once more
his voice arrested me: "Look yonder, and behold your own
Pentagonal house, and all its inmates."

I looked below,
and saw with my physical eye all that domestic individuality which I
had hitherto merely inferred with the understanding. And how poor and
shadowy was the inferred conjecture in comparison with the reality
which I now beheld! My four Sons calmly asleep in the North-Western
rooms, my two orphan Grandsons to the South; the Servants, the
Butler, my Daughter, all in their several apartments. Only my
affectionate Wife, alarmed by my continued absence, had quitted her
room and was roving up and down in the Hall, anxiously awaiting my
return. Also the Page, aroused by my cries, had left his room, and
under pretext of ascertaining whether I had fallen somewhere in a
faint, was prying into the cabinent in my study. All this I could now
see, not merely infer; and as we came nearer and nearer, I could
discern even the contents of my cabinet, and the two chests of gold
and the tablets of which the sphere had made mention.

Touched by my
Wife's distress, I would have sprung downward to reassure her, but I
found myself incapable of motion. "Trouble not yurself about
your Wife," said my Guide: "she will not be long left in
anxiety; meantime let us take a survey of Flatland."

Once more I
felt myself rising through space. It was even as the Sphere had said.
The further we receded from the object we beheld, the larger became
the field of vision. My native city, with the interior of every house
and every creature therein, lay open to my view in minature. We
mounted higher, and lo, the secrets of the earth, the depths of mines
and intermost caverns of the hills, were bared before me.

Awestruck at
the sight of the mysteries of the earth, thus unveiled before my
unworthy eye, I said to my Companion, "Behold, I am become as a
God. For the wise men in our country say that to see all things, or
as they express it, omnividence, is the attribute of God alone."
There was something of scorn in the voice of my Teacher as he made
answer: "is it so indeed? Then the very pick-pockets and cut-throats
of my country are to be worshiped by your wise men as being Gods:
for there is not one of them that does not see as much as you see
now. But trust me, your wise men are wrong."

I. Then is
omnividence the atribute of others besides Gods?

Sphere. I do
not know. But, if a pick-pocket or a cut-throat of our country can
see everything that is in your country, surely that is no reason why
the pick-pocket or cut-throat should be accepted by you as a God.
this omnividence, as you call it - it is not a common word in
Spaceland - does it make you more just, more merciful, less selfish,
more loving? Not in the least. Then how does it make you more divine?

I. "More
merciful, more loving!" But these are the qualities of women!
And we know that a Circle is a higher Being than a Straight Line, in
so far as knowledge and wisdom are more to be esteemed than mere affection.

Sphere. It is
not for me to classify human faculties according to merit. Yet many
of the best and wisest in Spaceland think more of the affections than
of the understanding, more of your despised Straight Lines than of
your belauded Circles. But enough of this. Look yonder. Do you know
that building?

I looked, and
afar off I saw an immense Polygonal structure, in which I recognized
the General Assembly Hall of the States of Flatland, surrounded by
dense lines of Pentagonal buildings at right angles to each other,
which I knew to be streets; and I perceived that I was approaching
the great Metropolis.

"Here we
descend," said my Guide. It was now morning, the first hour of
the first day of the two thousandth year of our era. Acting, as was
their wont, in strict accordance with precedent, the highest Circles
of the realm were meeting in solemn conclave, as they had met on the
first hour of the first day of the year 1000, and also on the first
hour of the first day of the year 0.

The minutes of
the previous meetings were now read by one whom I at once recognized
as my brother, a perfectly Symmetrical Square, and the Chief Clerk of
the High Council. It was found recorded on each occasion that:
"Whereas the States had been troubled by divers ill-intentioned
persons pretending to have received revelations from another World,
and professing to produce demonstrations whereby they had instigated
to frenzy both themselves and others, it had been for this cause
unanimously resolved by the Grand Council that on the first day of
each millenary, special injunctions be sent to the Prefects in the
several districts of Flatland, to make strict search for such
misguided persons, and without formality of mathematical examination,
to destroy all such as were Isosceles of any degree, to scourge and
imprison any regular Triangle, to cause any Square or Pentagon to be
sent to the district Asylum, and to arrest any one of higher rank,
sending him straightway to the Capital to be examined and judged by
the Council."

"You hear
your fate," said the Sphere to me, while the Council was passing
for the third time the formal resolution. "Death or imprisonment
awaits the Apostle of the Gospel of Three Dimensions." "Not
so," replied I, "the matter is now so clear to me, the
nature of real space so palpable, that methinks I could make a child
understand it. Permit me but to descend at this moment and enlighten
them." "Not yet," said my Guide, "the time will
come for that. Meantime I must perform my mission. Stay thou there in
thy place." Saying these words, he leaped with great dexterity
into the sea (if I may so call it) of Flatland, right in the midst of
the ring of Counsellors. "I come," cried he, "to
proclaim that there is a land of Three Dimensions."

I could see
many of the younger Counsellors start back in manifest horror, as the
Sphere's circular section widened before them. But on a sign from the
presiding Circle - who shewed not the slightest alarm or surprise -
six Isosceles of a low type from six different quarters rushed upon
the Sphere. "We have him," they cried; "No; yes; we
have him still! he's going! he's gone!"

"My
Lords," said the President to the Junior Circles of the Council,
"there is not the slightest need for surprise; the secret
archives, to which I alone have access, tell me that a similar
occurrence happened on the last two millennial commencements. You
will, of course, say nothing of these trifles outside the Cabinet."

Raising his
voice, he now summoned the guards. "Arrest the policemen; gag
them. You know your duty." After he had consigned to their fate
the wretched policemen - ill-fated and unwilling witnesses of a
State-secret which they were not to be permitted to reveal - he again
addressed the Counsellors. "My Lords, the business of the
Council being concluded, I have only to wish you a happy New
Year." Before departing, he expressed, at some length, to the
Clerk, my excellent but most unfortunate brother, his sincere regret
that, in accordance with precedent and for the sake of secrecy, he
must condemn him to perpetual imprisonment, but added his
satisfaction that, unless some mention were made by him of that day's
incident, his life would be spared.

19. How, though
the Sphere shewed me other mysteries of Spaceland, I still desired
more; and what came of it

WHEN I saw my
poor brother led away to imprisonment, I attempted to leap down into
the Council Chamber, desiring to intercede on his behalf, or at least
bid him farewell. But I found that I had no motion of my own. I
absolutely depended on the volition of my Guide, who said in gloomy
tones, "Heed not thy brother; haply thou shalt have ample time
hereafter to condole with him. Follow me."

Once more we
ascended into space. "Hitherto," said the Sphere, "I
have shown you naught save Plane Figures and their interiors. Now I
must introduce you to Solids, and reveal to you the plan upon which
they are constructed. Behold this multitude of moveable square cards.
See, I put one on another, not, as you supposed, Northward of the
other, but on the other. Now a second, now a third. See, I am
building up a Solid by a multitude of Squares parallel to one
another. Now the Solid is complete, being as high as it is long and
broad, and we call it a Cube."

"Pardon
me, my Lord," replied I; "but to my eye the appearance is
as of an Irregular Figure whose inside is laid open to the view; in
other words, methinks I see no Solid, but a Plane such as we infer in
Flatland; only of an Irregularity which betokens some monstrous
criminal, so that the very sight of it is painful to my eyes."

"True,"
said the Sphere, "it appears to you a Plane, because you are
not accustomed to light and shade and perspective; just as in
Flatland a Hexagon would appear a Straight Line to one who has not
the Art of Sight Recognition. But in reality it is a Solid, as you
shall learn by the sense of Feeling."

He then
introduced me to the Cube, and I found that this marvellous Being was
indeed no plane, but a Solid; and that he was endowed with six plane
sides and eight terminal points called solid angles; and I remembered
the saying of the Sphere that just such a Creature as this would be
formed by a Square moving, in Space, parallel to himself: and I
rejoiced to think that so insignificant a Creature as I could in some
sense be called the Progenitor of so illustrious an offspring.

But still I
could not fully understand the meaning of what my Teacher had told me
concerning "light" and "shade" and
"perspective"; and I did not hesitate to put my
difficulties before him.

Were I to give
the Sphere's explanation of these matters, succinct and clear though
it was, it would be tedious to an inhabitant of Space, who knows
these things already. Suffice it, that by his lucid statements, and
by changing the position of objects and lights, and by allowing me to
feel the several objects and even his own sacred Person, he at last
made all things clear to me, so that I could now readily distinguish
between a Circle and a Sphere, a Plane Figure and a Solid.

This was the
Climax, the Paradise, of my strange eventful History. Henceforth I
have to relate the story of my miserable Fall: - most miserable, yet
surely most undeserved! For why should the thirst for knowledge be
aroused, only to be disappointed and punished? My volition shrinks
from the painful task of recalling my humiliation; yet, like a second
Prometheus, I will endure this and worse, if by any means I may
arouse in the interiors of Plane and Solid Humanity a spirit of
rebellion against the Conceit which would limit our Dimensions to Two
or Three or any number short of Infinity. Away then with all personal
considerations! Let me continue to the end, as I began, without
further digressions or anticipations, pursuing the plain path of
dispassionate History. The exact facts, the exact words, - and they
are burnt in upon my brain, - shall be set down without alteration of
an iota; and let my Readers judge between me and Destiny.

The Sphere
would willingly have continued his lessons by indoctrinating me in
the conformation of all regular Solids, Cylinders, Cones, Pyramids,
Pentahedrons, Hexahedrons, Dodecahedrons, and Spheres: but I ventured
to interrupt him. Not that I was wearied of knowledge. On the
contrary, I thirsted for yet deeper and fuller draughts than he was
offering to me.

"Pardon
me," said I, "O Thou Whom I must no longer address as the
Perfection of all Beauty; but let me beg thee to vouchsafe thy
servant a sight of thine interior."

Sphere. My what?

I. Thine
interior: thy stomach, thy intestines.

Sphere. Whence
this ill-timed impertinent request? And what mean you by saying that
I am no longer the Perfection of all Beauty?

I. My Lord,
your own wisdom has taught me to aspire to One even more great, more
beautiful, and more closely approximate to Perfection than yourself.
As you yourself, superior to all Flatland forms, combine many Circles
in One, so doubtless there is One above you who combines many Spheres
in One Supreme Existence, surpassing even the Solids of Spaceland.
And even as we, who are now in Space, look down on Flatland and see
the insides of all things, so of a certainty there is yet above us
some higher, purer region, whither thou dost surely purpose to lead
me - O Thou Whom I shall always call, everywhere and in all
Dimensions, my Priest, Philosopher, and Friend - some yet more
spacious Space, some more dimensionable Dimensionality, from the
vantage-ground of which we shall look down together upon the revealed
insides of Solid things, and where thine own intestines, and those of
thy kindred Spheres, will lie exposed to the view of the poor
wandering exile from Flatland, to whom so much has already been vouchsafed.

Sphere. Pooh!
Stuff! Enough of this trifling! The time is short, and much remains
to be done before you are fit to proclaim the Gospel of Three
Dimensions to your blind benighted countrymen in Flatland.

I. Nay,
gracious Teacher, deny me not what I know it is in thy power to
perform. Grant me but one glimpse of thine interior, and I am
satisfied for ever, remaining henceforth thy docile pupil, thy
unemancipable slave, ready to receive all thy teachings and to feed
upon the words that fall from thy lips.

Sphere. Well,
then, to content and silence you, let me say at once, I would shew
you what you wish if I could; but I cannot. Would you have me turn my
stomach inside out to oblige you?

I. But my Lord
has shewn me the intestines of all my countrymen in the Land of Two
Dimensions by taking me with him into the Land of Three. What
therefore more easy than now to take his servant on a second journey
into the blessed region of the Fourth Dimension, where I shall look
down with him once more upon this land of Three Dimensions, and see
the inside of every three- dimensioned house, the secrets of the
solid earth, the treasures of the mines in Spaceland, and the
intestines of every solid living creature, even of the noble and
adorable Spheres.

Sphere. But
where is this land of Four Dimensions?

I. I know not:
but doubtless my Teacher knows.

Sphere. Not I.
There is no such land. The very idea of it is utterly inconceivable.

I. Not
inconceivable, my Lord, to me, and therefore still less inconceivable
to my Master. Nay, I despair not that, even here, in this region of
Three Dimensions, your Lordship's art may make the Fourth Dimension
visible to me; just as in the Land of Two Dimensions my Teacher's
skill would fain have opened the eyes of his blind servant to the
invisible presence of a Third Dimension, though I saw it not.

Let me recall
the past. Was I not taught below that when I saw a Line and inferred
a Plane, I in reality saw a Third unrecognized Dimension, not the
same as brightness, called "height"? And does it not now
follow that, in this region, when I see a Plane and infer a Solid, I
really see a Fourth unrecognized Dimension, not the same as colour,
but existent, though infinitesimal and incapable of measurement?

And besides
this, there is the Argument from Analogy of Figures.

Sphere.
Analogy! Nonsense: what analogy?

I. Your
Lordship tempts his servant to see whether he remembers the
revelations imparted to him. Trifle not with me, my Lord; I crave, I
thirst, for more knowledge. Doubtless we cannot see that other higher
Spaceland now, because we have no eye in our stomachs. But, just as
there was the realm of Flatland, though that poor puny Lineland
Monarch could neither turn to left nor right to discern it, and just
as there was close at hand, and touching my frame, the land of Three
Dimensions, though I, blind senseless wretch, had no power to touch
it, no eye in my interior to discern it, so of a surety there is a
Fourth Dimension, which my Lord perceives with the inner eye of
thought. And that it must exist my Lord himself has taught me. Or can
he have forgotten what he himself imparted to his servant?

In One
Dimension, did not a moving Point produce a Line with two terminal points?

In Two
Dimensions, did not a moving Line produce a Square with four terminal points?

In Three
Dimensions, did not a moving Square produce - did not this eye of
mine behold it - that blessed Being, a Cube, with eight terminal points?

And in Four
Dimensions shall not a moving Cube - alas, for Analogy, and alas for
the Progress of Truth, if it be not so - shall not, I say, the motion
of a divine Cube result in a still more divine Organization with
sixteen terminal points?

Behold the
infallible confirmation of the Series, 2, 4, 8, 16: is not this a
Geometrical Progression? Is not this - if I might quote my Lord's own
words - "strictly according to Analogy"?

Again, was I
not taught by my Lord that as in a Line there are two bounding
Points, and in a Square there are four bounding Lines, so in a Cube
there must be six bounding Squares? Behold once more the confirming
Series, 2, 4, 6: is not this an Arithmetical Progression? And
consequently does it not of necessity follow that the more divine
offspring of the divine Cube in the Land of Four Dimensions, must
have 8 bounding Cubes: and is not this also, as my Lord has taught me
to believe, "strictly according to Analogy"?

O, my Lord, my
Lord, behold, I cast myself in faith upon conjecture, not knowing the
facts; and I appeal to your Lordship to confirm or deny my logical
anticipations. If I am wrong, I yield, and will no longer demand a
fourth Dimension; but, if I am right, my Lord will listen to reason.

I ask
therefore, is it, or is it not, the fact, that ere now your
countrymen also have witnessed the descent of Beings of a higher
order than their own, entering closed rooms, even as your Lordship
entered mine, without the.opening of doors or windows, and appearing
and vanishing at will? On the reply to this question I am ready to
stake everything. Deny it, and I am henceforth silent. Only vouchsafe
an answer.

Sphere. (after
a pause). It is reported so. But men are divided in opinion as to the
facts. And even granting the facts, they explain them in different
ways. And in any case, however great may be the number of different
explanations, no one has adopted or suggested the theory of a Fourth
Dimension. Therefore, pray have done with this trifling, and let us
return to business.

I. I was
certain of it. I was certain that my anticipations would be
fulfilled. And now have patience with me and answer me yet one more
question, best of Teachers! Those who have thus appeared - no one
knows whence - and have returned - no one knows whither - have they
also contracted their sections and vanished somehow into that more
Spacious Space, whither I now entreat you to conduct me?

Sphere.
(moodily). They have vanished, certainly - if they ever appeared. But
most people say that these visions arose from the thought - you will
not understand me - from the brain; from the perturbed angularity of
the Seer.

I. Say they so?
Oh, believe them not. Or if it indeed be so, that this other Space is
really Thoughtland, then take me to that blessed Region where I in
Thought shall see the insides of all solid things. There, before my
ravished eye, a Cube, moving in some altogether new direction, but
strictly according to Analogy, so as to make every particle of his
interior pass through a new kind of Space, with a wake of its own -
shall create a still more perfect perfection than himself, with
sixteen terminal Extrasolid angles, and Eight solid Cubes for his
Perimeter. And once there, shall we stay our upward course? In that
blessed region of Four Dimensions, shall we linger on the threshold
of the Fifth, and not enter therein? Ah, no! Let us rather resolve
that our ambition shall soar with our corporal ascent. Then, yielding
to our intellectual onset, the gates of the Sixth Dimension shall fly
open; after that a Seventh, and then an Eighth -

How long I
should have continued I know not. In vain did the Sphere, in his
voice of thunder, reiterate his command of silence, and threaten me
with the direst penalties if I persisted. Nothing could stem the
flood of my ecstatic aspirations. Perhaps I was to blame; but indeed
I was intoxicated with the recent draughts of Truth to which he
himself had introduced me. However, the end was not long in coming.
My words were cut short by a crash outside, and a simultaneous crash
inside me, which impelled me through space with a velocity that
precluded speech. Down! down! down! I was rapidly descending; and I
knew that return to Flatland was my doom. One glimpse, one last and
never-to-be-forgotten glimpse I had of that dull level wilderness -
which was now to become my Universe again - spread out before my eye.
Then a darkness. Then a final, all- consummating thunderpeal; and,
when I came to myself, I was once more a common creeping Square, in
my Study at home, listening to the Peace-Cry of my approaching Wife.

20. How the
Sphere encouraged me in a Vision

ALTHOUGH I had
less than a minute for reflection, I felt, by a kind of instinct,
that I must conceal my experiences from my Wife. Not that I
apprehended, at the moment, any danger from her divulging my secret,
but I knew that to any Woman in Flatland the narrative of my
adventures must needs be unintelligible. So I endeavoured to reassure
her by some story, invented for the occasion, that I had accidentally
fallen through the trap-door of the cellar, and had there lain stunned.

The Southward
attraction in our country is so slight that even to a Woman my tale
necessarily appeared extraordinary and well- nigh incredible; but my
Wife, whose good sense far exceeds that of the average of her Sex,
and who perceived that I was unusually excited, did not argue with me
on the subject, but insisted that I was ill and required repose. I
was glad of an excuse for retiring to my chamber to think quietly
over what had happened. When I was at last by myself, a drowsy
sensation fell on me; but before my eyes closed I endeavoured to
reproduce the Third Dimension, and especially the process by which a
Cube is constructed through the motion of a Square. It was not so
clear as I could have wished; but I remembered that it must be
"Upward, and yet not Northward," and I determined
steadfastly to retain these words as the clue which, if firmly
grasped, could not fail to guide me to the solution. So mechanically
repeating, like a charm, the words, "Upward, yet not
Northward," I fell into a sound refreshing sleep.

During my
slumber I had a dream. I thought I was once more by the side of the
Sphere, whose lustrous hue betokened that he had exchanged his wrath
against me for perfect placability. We were moving together towards a
bright but infinitesimally small Point, to which my Master directed
my attention. As we approached, methought there issued from it a
slight humming noise as from one of your Spaceland blue-bottles, only
less resonant by far, so slight indeed that even in the perfect
stillness of the Vacuum through which we soared, the sound reached
not our ears till we checked our flight at a distance from it of
something under twenty human diagonals.

"Look
yonder," said my Guide, "in Flatland thou hast lived; of
Lineland thou hast received a vision; thou hast soared with me to the
heights of Spaceland; now, in order to complete the range of thy
experience, I conduct thee downward to the lowest depth of existence,
even to the realm of Pointland, the Abyss of No dimensions.

"Behold
yon miserable creature. That Point is a Being like ourselves, but
confined to the non-dimensional Gulf. He is himself his own World,
his own Universe; of any other than himself he can form no
conception; he knows not Length, nor Breadth, nor Height, for he has
had no experience of them; he has no cognizance even of the number
Two; nor has he a thought of Plurality; for he is himself his One and
All, being really Nothing. Yet mark his perfect self- contentment,
and hence learn this lesson, that to be self-contented is to be vile
and ignorant, and that to aspire is better than to be blindly and
impotently happy. Now listen."

He ceased; and
there arose from the little buzzing creature a tiny, low, monotonous,
but distinct tinkling, as from one of your Spaceland phonographs,
from which I caught these words, "Infinite beatitude of
existence! It is; and there is none else beside It."

"What,"
said I, "does the puny creature mean by it'?" "He
means himself," said the Sphere: "have you not noticed
before now, that babies and babyish people who cannot distinguish
themselves from the world, speak of themselves in the Third Person?
But hush!"

"It fills
all Space," continued the little soliloquizing Creature,
"and what It fills, It is. What It thinks, that It utters; and
what It utters, that It hears; and It itself is Thinker, Utterer,
Hearer, Thought, Word, Audition; it is the One, and yet the All in
All. Ah, the happiness ah, the happiness of Being!"

"Can you
not startle the little thing out of its complacency?" said I.
"Tell it what it really is, as you told me; reveal to it the
narrow limitations of Pointland, and lead it up to something
higher." "That is no easy task," said my Master;
"try you."

Hereon, raising
my voice to the uttermost, I addressed the Point as follows:

"Silence,
silence, contemptible Creature. You call yourself the All in All, but
you are the Nothing: your so-called Universe is a mere speck in a
Line, and a Line is a mere shadow as compared with - "
"Hush, hush, you have said enough," interrupted the Sphere,
"now listen, and mark the effect of your harangue on the King of Pointland."

The lustre of
the Monarch, who beamed more brightly than ever upon hearing my
words, shewed clearly that he retained his complacency; and I had
hardly ceased when he took up his strain again. "Ah, the joy,
ah, the joy of Thought! What can It not achieve by thinking! Its own
Thought coming to Itself, suggestive of Its disparagement, thereby to
enhance Its happiness! Sweet rebellion stirred up to result in
triumph! Ah, the divine creative power of the All in One! Ah, the
joy, the joy of Being!"

"You
see," said my Teacher, "how little your words have done. So
far as the Monarch understands them at all, he accepts them as his
own - for he cannot conceive of any other except himself - and plumes
himself upon the variety of Its Thought' as an instance of creative
Power. Let us leave this God of Pointland to the ignorant fruition of
his omnipresence and omniscience: nothing that you or I can do can
rescue him from his self-satisfaction."

After this, as
we floated gently back to Flatland, I could hear the mild voice of my
Companion pointing the moral of my vision, and stimulating me to
aspire, and to teach others to aspire. He had been angered at first -
he confessed - by my ambition to soar to Dimensions above the Third;
but, since then, he had received fresh insight, and he was not too
proud to acknowledge his error to a Pupil. Then he proceeded to
initiate me into mysteries yet higher than those I had witnessed,
shewing me how to construct Extra-Solids by the motion of Solids, and
Double Extra-Solids by the motion of Extra-Solids, and all
"strictly according to Analogy," all by methods so simple,
so easy, as to be patent even to the Female Sex.

21. How I tried
to teach the Theory of Three Dimensions to my Grandson, and with what success

I AWOKE
rejoicing, and began to reflect on the glorious career before me. I
would go forth, methought, at once, and evangelize the whole of
Flatland. Even to Women and Soldiers should the Gospel of Three
Dimensions be proclaimed. I would begin with my Wife.

Just as I had
decided on the plan of my operations, I heard the sound of many
voices in the street commanding silence. Then followed a louder
voice. It was a herald's proclamation. Listening attentively, I
recognized the words of the Resolution of the Council, enjoining the
arrest, imprisonment, or execution of any one who should pervert the
minds of the people by delusions, and by professing to have received
revelations from another World.

I reflected.
This danger was not to be trifled with. It would be better to avoid
it by omitting all mention of my Revelation, and by proceeding on the
path of Demonstration - which after all, seemed so simple and so
conclusive that nothing would be lost by discarding the former means.
"Upward, not Northward" - was the clue to the whole proof.
It had seemed to me fairly clear before I fell asleep; and when I
first awoke, fresh from my dream, it had appeared as patent as
Arithmetic; but somehow it did not seem to me quite so obvious now.
Though my Wife entered the room opportunely just at that moment, I
decided, after we had exchanged a few words of commonplace
conversation, not to begin with her.

My Pentagonal
Sons were men of character and standing, and physicians of no mean
reputation, but not great in mathematics, and, in that respect, unfit
for my purpose. But it occurred to me that a young and docile
Hexagon, with a mathematical turn, would be a most suitable pupil.
Why therefore not make my first experiment with my little precocious
Grandson, whose casual remarks on the meaning of $3^3$ had met with
the approval of the Sphere? Discussing the matter with him, a mere
boy, I should be in perfect safety; for he would know nothing of the
Proclamation of the Council; whereas I could not feel sure that my
Sons - so greatly did their patriotism and reverence for the Circles
predominate over mere blind affection - might not feel compelled to
hand me over to the Prefect, if they found me seriously maintaining
the seditious heresy of the Third Dimension.

But the first
thing to be done was to satisfy in some way the curiosity of my Wife,
who naturally wished to know something of the reasons for which the
Circle had desired that mysterious interview, and of the means by
which he had entered the house. Without entering into the details of
the elaborate account I gave her, - an account, I fear, not quite so
consistent with truth as my Readers in Spaceland might desire, - I
must be content with saying that I succeeded at last in persuading
her to return quietly to her household duties without eliciting from
me any reference to the World of Three Dimensions. This done, I
immediately sent for my Grandson; for, to confess the truth, I felt
that all that I had seen and heard was in some strange way slipping
away from me, like the image of a half-grasped, tantalizing dream,
and I longed to essay my skill in making a first disciple.

When my
Grandson entered the room I carefully secured the door. Then, sitting
down by his side and taking our mathematical tablets, - or, as you
would call them, Lines - I told him we would resume the lesson of
yesterday. I taught him once more how a Point by motion in One
Dimension produces a Line, and how a straight Line in Two Dimensions
produces a Square. After this, forcing a laugh, I said, "And
now, you scamp, you wanted to make me believe that a Square may in
the same way by motion Upward, not Northward' produce another figure,
a sort of extra Square in Three Dimensions. Say that again, you young rascal."

At this moment
we heard once more the herald's "O yes! O yes!" outside in
the street proclaiming the Resolution of the Council. Young though he
was, my Grandson - who was unusually intelligent for his age, and
bred up in perfect reverence for the authority of the Circles - took
in the situation with an acuteness for which I was quite unprepared.
He remained silent till the last words of the Proclamation had died
away, and then, bursting into tears, "Dear Grandpapa," he
said, "that was only my fun, and of course I meant nothing at
all by it; and we did not know anything then about the new Law; and I
don't think I said anything about the Third Dimension; and I am sure
I did not say one word about Upward, not Northward,' for that would
be such nonsense, you know. How could a thing move Upward, and not
Northward? Upward and not Northward! Even if I were a baby, I could
not be so absurd as that. How silly it is! Ha! ha! ha!"

"Not at
all silly," said I, losing my temper; "here for example, I
take this Square," and, at the word, I grasped a moveable
Square, which was lying at hand - "and I move it, you see, not
Northward but - yes, I move it Upward - that is to say, not
Northward, but I move it somewhere - not exactly like this, but
somehow - " Here I brought my sentence to an inane conclusion,
shaking the Square about in a purposeless manner, much to the
amusement of my Grandson, who burst out laughing louder than ever,
and declared that I was not teaching him, but joking with him; and so
saying he unlocked the door and ran out of the room. Thus ended my
first attempt to convert a pupil to the Gospel of Three Dimensions.

22. How I then
tried to diffuse the Theory of Three Dimensions by other means, and
of the result

MY FAILURE with
my Grandson did not encourage me to communicate my secret to others
of my household; yet neither was I led by it to despair of success.
Only I saw that I must not wholly rely on the catch-phrase,
"Upward, not Northward," but must rather endeavour to seek
a demonstration by setting before the public a clear view of the
whole subject; and for this purpose it seemed necessary to resort to writing.

So I devoted
several months in privacy to the composition of a treatise on the
mysteries of Three Dimensions. Only, with the view of evading the
Law, if possible, I spoke not of a physical Dimension, but of a
Thoughtland whence, in theory, a Figure could look down upon Flatland
and see simultaneously the insides of all things, and where it was
possible that there might be supposed to exist a Figure environed, as
it were, with six Squares, and containing eight terminal Points. But
in writing this book I found myself sadly hampered by the
impossibility of drawing such diagrams as were necessary for my
purpose; for of course, in our country of Flatland, there are no
tablets but Lines, and no diagrams but Lines, all in one straight
Line and only distinguishable by difference of size and brightness;
so that, when I had finished my treatise (which I entitled,
"Through Flatland to Thoughtland") I could not feel certain
that many would understand my meaning.

Meanwhile my
life was under a cloud. All pleasures palled upon me; all sights
tantalized and tempted me to outspoken treason, because I could not
but compare what I saw in Two Dimensions with what it really was if
seen in Three, and could hardly refrain from making my comparisons
aloud. I neglected my clients and my own business to give myself to
the contemplation of the mysteries which I had once beheld, yet which
I could impart to no one, and found daily more difficult to reproduce
even before my own mental vision.

One day, about
eleven months after my return from Spaceland, I tried to see a Cube
with my eye closed, but failed; and though I succeeded afterwards, I
was not then quite certain (nor have I been ever afterwards) that I
had exactly realized the original. This made me more melancholy than
before, and determined me to take some step; yet what, I knew not. I
felt that I would have been willing to sacrifice my life for the
Cause, if thereby I could have produced conviction. But if I could
not convince my Grandson, how could I convince the highest and most
developed Circles in the land?

And yet at
times my spirit was too strong for me, and I gave vent to dangerous
utterances. Already I was considered heterodox if not treasonable,
and I was keenly alive to the danger of my position; nevertheless I
could not at times refrain from bursting out into suspicious or
half-seditious utterances, even among the highest Polygonal and
Circular society. When, for example, the question arose about the
treatment of those lunatics who said that they had received the power
of seeing the insides of things, I would quote the saying of an
ancient Circle, who declared that prophets and inspired people are
always considered by the majority to be mad; and I could not help
occasionally dropping such expressions as "the eye that discerns
the interiors of things," and "the all-seeing land";
once or twice I even let fall the forbidden terms "the Third and
Fourth Dimensions." At last, to complete a series of minor
indiscretions, at a meeting of our Local Speculative Society held at
the palace of the Prefect himself, - some extremely silly person
having read an elaborate paper exhibiting the precise reasons why
Providence has limited the number of Dimensions to Two, and why the
attribute of omnividence is assigned to the Supreme alone - I so far
forgot myself as to give an exact account of the whole of my voyage
with the Sphere into Space, and to the Assembly Hall in our
Metropolis, and then to Space again, and of my return home, and of
everything that I had seen and heard in fact or vision. At first,
indeed, I pretended that I was describing the imaginary experiences
of a fictitious person; but my enthusiasm soon forced me to throw of
all disguise, and finally, in a fervent peroration, I exhorted all my
hearers to divest themselves of prejudice and to become believers in
the Third Dimension.

Need I say that
I was at once arrested and taken before the Council?

Next morning,
standing in the very place where but a very few months ago the Sphere
had stood in my company, I was allowed to begin and to continue my
narration unquestioned and uninterrupted. But from the first I
foresaw my fate; for the President, noting that a guard of the better
sort of Policemen was in attendance, of angularity little, if at all,
under 55°, ordered them to be relieved before I began my
defence, by an inferior class of 2° or 3°. I knew only too
well what that meant. I was to be executed or imprisoned, and my
story was to be kept secret from the world by the simultaneous
destruction of the officials who had heard it; and, this being the
case, the President desired to substitute the cheaper for the more
expensive victims.

After I had
concluded my defence, the President, perhaps perceiving that some of
the junior Circles had been moved by my evident earnestness, asked me
two questions: -

1. Whether I
could indicate the direction which I meant when I used the words
"Upward, not Northward"?

2. Whether I
could by any diagrams or descriptions (other than the enumeration of
imaginary sides and angles) indicate the Figure I was pleased to call
a Cube?

I declared that
I could say nothing more, and that I must commit myself to the Truth,
whose cause would surely prevail in the end.

The President
replied that he quite concurred in my sentiment, and that I could not
do better. I must be sentenced to perpetual imprisonment; but if the
Truth intended that I should emerge from prison and evangelize the
world, the Truth might be trusted to bring that result to pass.
Meanwhile I should be subjected to no discomfort that was not
necessary to preclude escape, and, unless I forfeited the privilege
by misconduct, I should be occasionally permitted to see my brother
who had preceded me to my prison.

Seven years
have elapsed and I am still a prisoner, and - if I except the
occasional visits of my brother - debarred from all companionship
save that of my jailers. My brother is one of the best of Squares,
just, sensible, cheerful, and not without fraternal affection; yet I
confess that my weekly interviews, at least in one respect, cause me
the bitterest pain. He was present when the Sphere manifested himself
in the Council Chamber; he saw the Sphere's changing sections; he
heard the explanation of the phenomena then given to the Circles.
Since that time, scarcely a week has passed during seven whole years,
without his hearing from me a repetition of the part I played in that
manifestation, together with ample descriptions of all the phenomena
in Spaceland, and the arguments for the existence of Solid things
derivable from Analogy. Yet - I take shame to be forced to confess it
- my brother has not yet grasped the nature of the Third Dimension,
and frankly avows his disbelief in the existence of a Sphere.

Hence I am
absolutely destitute of converts, and, for aught that I can see, the
millennial Revelation has been made to me for nothing. Prometheus up
in Spaceland was bound for bringing down fire for mortals, but I -
poor Flatland Prometheus - lie here in prison for bringing down
nothing to my countrymen. Yet I exist in the hope that these memoirs,
in some manner, I know not how, may find their way to the minds of
humanity in Some Dimension, and may stir up a race of rebels who
shall refuse to be confined to limited Dimensionality.

That is the
hope of my brighter moments. Alas, it is not always so. Heavily
weighs on me at times the burdensome reflection that I cannot
honestly say I am confident as to the exact shape of the once- seen,
oft-regretted Cube; and in my nightly visions the mysterious precept,
"Upward, not Northward," haunts me like a soul-devouring
Sphinx. It is part of the martyrdom which I endure for the cause of
the Truth that there are seasons of mental weakness, when Cubes and
Spheres flit away into the background of scarce-possible existences;
when the Land of Three Dimensions seems almost as visionary as the
Land of One or None; nay, when even this hard wall that bars me from
my freedom, these very tablets on which I am writing, and all the
substantial realities of Flatland itself, appear no better than the
offspring of a diseased imagination, or the baseless fabric of a dream.

Footnotes

The Author
desires me to add, that the misconception of some of his critics on
this matter has induced him to insert in his dialogue with the
Sphere, certain remarks which have a bearing on the point in
question, and which he had previously omitted as being tedious and unnecessary.

"What need
of a certificate?" a Spaceland critic may ask: "Is not the
procreation of a Square Son a certificate from Nature herself,
proving the Equalsidedness of the Father?" I reply that no Lady
of any position will marry an uncertified Triangle. Square offspring
has sometimes resulted from a slightly Irregular Triangle; but in
almost every such case the Irregularity of the first generation is
visited on the third; which either fails to attain the Pentagonal
rank, or relapses to the Triangular.

When I was in
Spaceland I understood that some of your Priestly circles have in the
same way a separate entrance for Farmers, Villagers and Teachers of
Board Schools (Spectator, Sept. 1884, p. 1255) that they may
"approach in a becoming and respectful manner."

When I say
"sitting," of course I do not mean any change of attitude
such as you in Spaceland signify by that word: for as we have no
feet, we can no more "sit" nor "stand" (in your
sense of the word) than one of your soles or flounders.

Nevertheless,
we perfectly well recognize the different mental states of volition
implied in "lying," "sitting," and
"standing," which are to some extent indicated to a
beholder by a slight increase of lustre corresponding to the increase
of volition.

But on this,
and a thousand other kindred subjects, time forbids me to dwell.